"Genetic variants associated with breast size also influence breast cancer risk", Eriksson et al 2012 http://bmcmedgenet.biomedcentral.com/articles/10.1186/1471-2350-13-53
"we conducted a genome-wide association study (GWAS) of self-reported bra cup size, controlling for age, genetic ancestry, breast surgeries, pregnancy history and bra band size, in a cohort of 16,175 women of European ancestry.
Results: We identified seven single-nucleotide polymorphisms (SNPs) significantly associated with breast size (p<5·10−8): rs7816345 near ZNF703, rs4849887 and (independently) rs17625845 flanking INHBB, rs12173570 near ESR1, rs7089814 in ZNF365, rs12371778 near PTHLH, and rs62314947 near AREG. Two of these seven SNPs are in linkage disequilibrium (LD) with SNPs associated with breast cancer (those near ESR1 and PTHLH), and a third (ZNF365) is near, but not in LD with, a breast cancer SNP. The other three loci (ZNF703, INHBB, and AREG) have strong links to breast cancer, estrogen regulation, and breast development.
Conclusions: These results provide insight into the genetic factors underlying normal breast development and show that some of these factors are shared with breast cancer.
...The relationship between breast size and cancer is not entirely clear. Two studies have found that, for lean women, larger breast size is associated with a higher risk of breast cancer [7, 8]. For example, Kusano et al. [7] found that among women with a BMI under 25, those with a cup size of D or larger had a 1.8 times higher risk of breast cancer than those with a cup size of A or smaller.
Genetic factors also play a role in breast cancer risk, with many genetic associations discovered to date. In contrast, there have been no genetic studies of breast size and only one GWAS of breast density [9]. Twin studies have shown that breast size is about 56% heritable, with only about a third of this heritability shared with the heritability of obesity [10]
- 10. Wade TD, Zhu G, Martin NG: "Body mass index and breast size in women: same or different genes?" https://www.researchgate.net/profile/Tracey_Wade2/publication/46576952_Body_Mass_Index_and_Breast_Size_in_Women_Same_or_Different_Genes/links/00b7d52fbf89094b60000000.pdf . Twin Res Hum Genet. 2010, 13: 450-454. 10.1375/twin.13.5.450.
...Subsets of participants also reported other phenotypes. As covariates in the analysis, we included the projections onto the first five principal components of genetic ancestry as well as age, bra band size (in inches), and indicator variables for breast augmentation surgery, breast reduction surgery, mastectomy, past pregnancy, and current pregnancy or breastfeeding. Out of the 16,175 participants, all but 3 reported age, over 15,000 reported bra band size, about 12,000 reported breast surgery status (augmentation, reduction, mastectomy, or none), about 6,000 reported if they had ever been pregnant, and 4,000 reported if they were currently pregnant or breastfeeding.
Band size was used as a covariate instead of BMI because while almost every participant reported band size, only about half reported BMI. Band size has previously been used as a proxy for BMI in breast size research [8]. The correlation between BMI and band size in our sample was over 0.5. Furthermore, although bra size is easy to report, it is not a perfect proxy for actual breast volume. There is evidence that controlling for bra band size improves the correlation between cup size and breast volume [19].
...Bra size was coded from 0 to 9, corresponding to the categories: Smaller than AAA, AAA, AA, A, B, C, D, DD, DDD, and Larger than DDD, respectively. Mean size was 4.99 (just under a “C” cup) and the standard deviation was 1.45.
...On average, those reporting augmentation reported 0.5 size smaller breasts, reduction 1 size bigger, mastectomy 0.5 size smaller, and ever pregnant 0.1 size bigger. For every inch of band size, cup size was reported to be 0.1 sizes bigger on average
....There is a strong relationship in our data between BMI and breast size—each additional BMI unit corresponds to an increase of about 0.1 cup sizes on average. However, the SNPs in Table 1 are not in LD with any variants previously associated with BMI [35]; this is expected due to the inclusion of bra band size (which is correlated with BMI) as a covariate. Furthermore, even if we did not control for BMI, the strongest associations with BMI (e.g., rs1558902 near FTO) have effects of about 0.4 BMI units per allele. This would correspond to an expected βof about 0.04 for breast size for these SNPs, which is below the effect sizes we are powered to detect here. Indeed, if bra band size is not included as a covariate, rs1558902 has an estimated β of 0.07 (95% CI: 0.04 – 0.10) for breast size and p-value of 8·10−6as compared to βof 0.04 (95% CI: 0.01 – 0.07) with bra band size included.
The covariates included in the analysis explain about 9.7% of the variance in breast size in our data; including the 7 SNPs in Table 1 that are genome-wide significant increases this to 10.9%. We used these 7 SNPs to compute a genetic propensity score for breast size by counting the number of alleles associated with larger size that each participant carried. The average cup size among women in the top 5% of this score (women carrying 9 or more of the 14 possible “large” alleles) was 0.83 cup sizes bigger (5.39 versus 4.56) than the average cup size among women in the bottom 5% of this score (women carrying 4 or fewer “large” alleles)."
[An interesting start but leaves out a lot of desirable results: no GCTA estimate, no polygenic score of variance explained by all SNPs, no genetic correlations with BMI or breast cancer.]
"Large-scale genotyping identifies a new locus at 22q13.2 associated with female breast size", Li et al 2013 https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4159740/
"The samples consisted of the Swedish KARMA, LIBRO-1 and SASBAC studies genotyped on iCOGS, a custom illumina iSelect genotyping array comprising of 211,155 single nucleotide polymorphisms (SNPs) designed for replication and fine mapping of common and rare variants with relevance to breast, ovary and prostate cancer. Breast size of each subject was ascertained by measuring total breast area (mm2) on a mammogram.
Results: We confirm genome-wide significant associations at 8p11.23 (rs10086016, P = 1.3 × 10−14) and report a new locus at 22q13 (rs5995871, P = 3.2 × 10−8). The latter region contains the MKL1 gene, which has been shown to impact endogenous estrogen-receptor α transcriptional activity and is recruited on estradiol-sensitive genes. We also replicated previous GWAS findings for breast size at four other loci.
To evaluate whether there is any genetic overlap between mammographic breast area and breast cancer risk, polygenic scores (based on mammographic breast area) were calculated according to the methods by Purcell et al. [22] to test the combined effect of multiple weak associations across the genome. The SASBAC data, which has screen film mammograms for both breast cancer cases and controls, were used. In order to identify polygenic effects due to independent SNPs in linkage equilibrium with one another, we performed the analysis using a pruned dataset (51,303 SNPs). Linkage equilibrium-based SNP pruning was performed using the --indep-pairwise function (window size in SNPs: 1,500; the number of SNPs to shift the window at each step: 150; r2 threshold: 0.2) in Plink [10]. KARMA, the study with the most number of samples (n=3,420) was used as a reference dataset for computing polygenic scores. Ten sets of SNPs were generated from the mammographic breast area association results at Pvalue thresholds of 0.0001, 0.001, 0.01, 0.05, 0.1, 0.2, 0.3, 0.4, 0.5 and 1.0. Each subject was then scored using the sum of the number of reference alleles multiplied by the corresponding beta estimate from the mammographic breast area GWAS for the alleles in each of the SNP sets. Logistic regression was used compare the polygenic scores between breast cancer cases and controls. All models were adjusted for age at mammogram and BMI.
Estimation of the phenotypic variance explained by common variants for 1,206 subjects genotyped on both the iCOGS and Illumina HumanHap300 BeadChip was performed using the REML method described in Yang et al [23]. The estimate of variance explained for breast cancer was transformed from the observed scale to that on the underlying scale based on a specified prevalence rate of 0.0189.
Breast size was ascertained as the breast area on a mammogram in mm2. Mammograms of the cranial-caudal view in the KARMA and LIBRO-1 studies were automatically thresholded to find the breast edge and measured using ImageJ (Supplementary Figures 1 and 2). Mammograms of the medio-lateral oblique view in the SASBAC study were manually outlined by one reader to delineate the breast edge and exclude the pectoral muscle being before measured using Cumulus (Supplementary Figure 3).
Table 1: mean(SD) breast sizes/area/cross-section in cm^2:
n=3420 137.2 (58.0)
n=2243 124.4 (43.3)
n=1506 171.6 (54.3)
[rough means: 140(52.6)]
Only two SNPs showed genome-wide significant associations and consistent evidence of replication across all 3 datasets (rs10086016, P = 1.3 × 10−14, beta=-0.16; I2= 0; Phet=0.54 and rs5995871, P=3.2 × 10−8, beta=-0.13; I2= 0; Phet=0.94, Table 2) under the additive model.
...We also identified a novel locus at 22q13.2 (rs5995871, genotyped SNP with smallest Pvalue) which reached genome-wide significance at P = 3.2 × 10−8, mapping within MKL1. Imputation of 1KGP SNPs yielded multiple variants associated with total mammographic breast area, with the lowest P-value observed at rs73169028 (P= 1.22 × 10-8). This SNP was in high LD with rs5995871 (R-sq=0.833; D′=0.913). In conditional regression analyses, rs5995871 was sufficient to account for all association signals within the locus (±500 kb, Supplementary Figure 5). No heterogeneity in the beta estimates was observed for either locus across all three studies. A list of all genotyped SNPs which passed the suggestive threshold of P<1 × 10-5 is given in Supplementary Table 2. Five other SNPS (rs4849887 and rs17625845 near INHBB, rs12173570 near ESR1, rs7089814 in ZNF365, rs12371778 near PTHLH) that have previously been reported to be associated with bra size were also found to be associated with total mammographic breast area in our study at P<0.05 (Supplementary Table 3).
...Allele frequency differences by breast size were observed among both European and Asian populations for the top hits in the 8p11.23 and 22q13.2 regions. Every additional copy of rs10086016(C) and rs5995871(G) was associated with smaller total mammographic breast area. The frequencies of these alleles were both lower for the European CEU population (each ∼12%), than for the Asian CHB and JPT populations on HapMap (ranging between 24.5% to 38.6%) (Supplementary Table 4)...It is possible that the allele frequency differences for the top hits in both the 8p11.23 and 22q13.2 regions are linked to ethnic differences in breast size. Asian women tend to have smaller breasts on average when compared to Caucasian women [31]. In this study, we observed that the effect alleles of the two common variants which were found to be associated with smaller total mammographic breast area to be more common amongst the Chinese and Japanese HapMap populations compared to Europeans. However, it should be noted that since these SNPs explain only about 1% of the variance for breast size, a relatively slight difference in allelic frequency may explain only a small fraction of the actual phenotype.
...Given that there is a public interest in knowing whether there is a link between breast size and breast cancer, we examined whether breast cancer susceptibility loci were associated with mammographic breast size. In the landmark breast cancer large-scale genotyping association analysis involving more than 100,000 women conducted by the Breast Cancer Association Consortium (BCAC), 67 known and novel breast cancer susceptibility loci were reported [9]. Of the 13 breast cancer susceptibility loci associated (at P<0.05) with mammographic breast area only six SNPs showed a consistent (the allele associated with large size being also associated with breast cancer risk) direction of association (Table 3 and Supplementary Table 5). In a lookup of our top genotyped SNPs for total mammographic breast area in the consortium data, rs10086016(C) and rs5995871(G) were found to be associated with overall breast cancer risk (odds ratio [95% confidence interval]) of 0.95 (0.93 to 0.97) and 1.12 (1.09 to 1.15), respectively. Both SNPs were associated with a decrease in total mammographic breast area. Whilst polygenic scores derived from the “top” SNPs for association with total mammographic breast area in the KARMA dataset were found to be significantly associated with the same trait in the SASBAC dataset for Pvalue thresholds between 0.1 and 1 (P<0.05, Supplementary Figure 6), the smallest pvalue for association with breast cancer risk in the same dataset was 0.14.
...We also evaluated the proportion of phenotypic variance that could possibly be explained by all SNPs present on the current genotyping array used. For a subset of the SASBAC study (n=1,206), we had genetic data generated from both the customized iCOGS chip and the commercial Infinium HumanHap300 BeadChip. We estimated the proportion of phenotypic variance for mammographic breast area explained by all SNPs on each chip to be 0.31 (iCOGS, SE=0.16) and 0.47 (Illumina, SE=0.25), respectively (Supplementary Table 6). For breast cancer, the estimated proportion of phenotypic variance explained were 0.57 (iCOGS, SE=0.11) and 0.32 (Illumina, SE=0.17), respectively.
...Study findings on a potential link between breast size and breast cancer are mixed. Some studies have found that larger breast sizes are associated with increased risk of cancer, while others have found no link between breast size and cancer risk [32-35]. We expanded the analysis carried out by Eriksson et al. [5] to include 67 novel and known breast cancer susceptibility SNPs reported in a landmark paper on a mega-consortium effort (COGS) to identify breast cancer susceptibility variants [9] and found 13 breast cancer SNPs to be associated with breast size at P<0.05, suggesting that there is a significant overlap among SNPs for breast size and breast cancer risk (P=2.91 × 10-7 in a two-tailed test of population proportion where the alternate hypothesis is that the true proportion is not equal to 5% as expected by chance). It is however, notable that the effects of 6 of the 13 SNPs were in opposite directions for breast size and breast cancer risk. Although we have found evidence that there is a connection between genetic determinants of breast size and breast cancer risk, our results show that larger breast size are not necessarily associated with an increase breast cancer risk. On the iCOGS chip which has been customized to study genetic variants predisposing to breast cancer, we also saw no evidence of a shared polygenic component between mammographic breast area and the disease, suggesting that caution should be exercised when interpreting any positive correlation between these two phenotypes."
[If these GCTAs are right, breast size is almost entirely additive: the twin study was ~0.5, the better GCTA is also almost ~0.5. The estimated effect sizes are also quite large: the top alleles account for a tenth of cup size each, indicating that are likely not that many variants involved. If so, it should respond to any selection for larger breasts very quickly, yet hasn't. The racial differences on both the phenotype and genetic levels also suggests selection for different levels in different places. Larger breasts, aside from the breast cancer issue which shouldn't affect reproductive fitness too much historically (especially compared to child birth mortality), seem like they would come with penalties: more back pain, less athleticism, added metabolic expense of the additional ounces of flesh, more resources while growing. Differing intensity of sexual selection might explain why more or less expensive secondary sex characteristics?
At a narrow-sense SNP heritability of 0.47 and population mean of breast size area 140(52.6) cm^2, upper bounds on the efficacy of selection are 39cm^2 with 10 embryos and 26cm^2 with a more realistic 4:
embryoScores <- function(n, variance) { rnorm(n, mean=0, sd=sqrt(variance*0.5)); }
embryoSelectionGain <- function(n, variance) { scores <- embryoScores(n, variance)
return(max(scores) - mean(scores)); }
simEmbryoSelection <- function(n=2, variance=0.47, iters=100000) { replicate(iters, embryoSelectionGain(n, variance)); }
mean(simEmbryoSelection(n=10))
# [1] 0.7469298563
mean(simEmbryoSelection(n=10)) * 52.6
# [1] 39.28784006
mean(simEmbryoSelection(n=4)) * 52.6
# [1] 26.25772435
23andMe paper: top 7 SNPs have an incremental variance explained of 10.9% - 9.7% = 1.2%, so:
mean(simEmbryoSelection(n=4, variance=0.012)) * 52.6
[1] 4.193488721
Li et al 2013 doesn't report the variance explained by their polygenic scores in the paper or supplemental material, but as their sample is half the size of the 23andMe sample, and they only report 1 new genome-wide statistically-significant hit, we could guess that their polygenic score meta-analyzed with the 23andMe polygenic score would only increase it by half, to 1.8%:
R> mean(simEmbryoSelection(n=4, variance=0.018))
[1] 0.09767069559
R> 0.09767069559 * 52.6
[1] 5.137478588
R> 0.09767069559 * 1.45
[1] 0.1416225086
So we could expect a 0.097SD increase in cup size or area in cm^2.
What value is that? We can extrapolate from beast augmentation (https://en.wikipedia.org/wiki/Breast_augmentation): if many women are willing to pay thousands of dollars for plastic surgery, despite the unpleasantness of surgery, the risk of complications, the chance of the implants bursting within a few years and needing to be monitored and eventually surgically removed or replaced, the potential social stigma, and the willingness to take such a measure in the first place, then the value to them must be extremely high, as indicated by post-operative increases in self-esteem and libido (https://en.wikipedia.org/wiki/Breast_augmentation#Mental_health).
And many find it worthwhile; as one of the most popular cosmetic surgeries (second most popular in 2015 after liposuction http://www.surgery.org/media/news-releases/american-society-for-aesthetic-plastic-surgery-reports-more-than-135-billion-spent-for-the-first-time-ever, 305856 procedures done costing \$1,191,025,070, average $3,497/$3,964 http://www.surgery.org/sites/default/files/ASAPS-Stats2015.pdf) ), perhaps as many as 4% of all American women have had breast augmentation surgery (https://fivethirtyeight.com/datalab/dear-mona-what-percentage-of-women-have-breast-implants/).
So if 4% of women are willing to pay ~$3750 for breast augmentation surgery, and we assume that the value to the rest is exactly $0 (to be conservative, although we can imagine that many women would be happy if they woke up with larger breasts), then the expected loss of the surgery is 0.04*3750=$150 and so the value must be >$150.
How much does the surgery increase cup size or area in cm^2 on average?
Hard sources are scarce and the target cup size or CC volume of an implant will differ based on each woman's desires, body size, breast shape, etc; but reading through plastic surgeon websites and discussions, it seems that ~100-300 CC yielding an increase of 1-2 cups is the common target and no larger.
If 1 cup is worth >$150, then one would expect a genetic gain of 0.14 cups to be worth 0.14*150>$21 in future gains.
The reported mean age of breast augmentation surgery users is 34, so arguably we should discount that >$21 by 34 years to compare to the present-day cost of embryo selection, so its net present value would be >21 / (1 + 0.05)^34 = >$4 (using my usual 5% discount rate). On the other hand, the value of larger breasts also arguably starts in puberty, and American girls begin puberty ~9.5yo in 2013 (http://www.reuters.com/article/us-girls-puberty-idUSBRE9A304D20131104), in which case it'd be more like >$13.
What factors have I left out? The main ones seem to be the possible increase in breast cancer, and the definite increase in BMI.
The minimal increase in breast cancer in Li et al 2013 seems to somewhat contradict Eriksson et al 2012's results, and indicates no net effect.
Wade et al 2010 finds that https://www.researchgate.net/profile/Tracey_Wade2/publication/46576952_Body_Mass_Index_and_Breast_Size_in_Women_Same_or_Different_Genes/links/00b7d52fbf89094b60000000.pdf
> the AE model gave the best fit and the proportions of variance explained by the latent sources of A and E are shown in Figure 2. It can be seen that only 15% of the variance of bra cup size is due to the additive genetic sources contributing to BMI with a further 41% of genetic variance specific to BRA. The correlation between genetic sources contributing to BMI and bra cup was 0.52 and the correlation for non-shared environmental sources was 0.44
15.1/40.8=0.37, so I believe that for every 1 SD we increase bra size by selection (without any selection against BMI), we should expect to increase BMI by 0.37SD.
So if we can increase bra size by 0.097SD, then we would also wind up increasing BMI by 0.00359 SD.
In my embryo selection essay, I used http://vinecon.ucdavis.edu/publications/cwe1201.pdf "The Marginal External Cost of Obesity in the United States", Parks et al 2012 to estimate the cost of 1 SD of BMI at$3586; so the cost of the BMI increase is $128.
The good news is that BMI polygenic scores work much better than breast polygenic scores, with the highest one at 15.3%. So we can more than undo the effect of breast selection on BMI:
R> mean(simEmbryoSelection(n=4, variance=0.153))
[1] 0.2845980551
R> mean(simEmbryoSelection(n=4, variance=0.153)) * 3586
[1] 1020.913556
However, that doesn't necessarily mean we want to do any selection on breast at all: the cost in BMI may be too high. We can undo that 0.00359SD of BMI increase but maybe it's worth more if we selected on BMI alone?
We can say that the cost of the BMI increase is $128, and I already estimated the breast value at >$21; but the lower bound is not tight. It could easily exceed $128, in which case we do want to do selection on both traits.
On the other hand, there remains the issue of breast cancer, one could plausibly argue that the cost of BMI may keep going up over time, that larger breasts may or may not be helpful but always have drawbacks like back pain and less athleticism, from a sexual attractiveness point of view slenderness is more reliably & universally appealing, and that if one is going to do embryo selection for attractiveness at all, it would probably be better to select for height, lower BMI, and hair/eye color.
True, it costs next to nothing to incorporate breast size as a trait in an existing embryo selection (since the SNP array will doubtless have most of the relevant SNPs on it), but the genetic correlation with BMI makes it a questionable thing to select on, especially compared to something like IQ where almost all of the genetic correlations are in desirable directions and so it's underestimated if anything.
On net, selection for breast size probably isn't a good idea at this point without stronger polygenic scores for BMI.
"we conducted a genome-wide association study (GWAS) of self-reported bra cup size, controlling for age, genetic ancestry, breast surgeries, pregnancy history and bra band size, in a cohort of 16,175 women of European ancestry.
Results: We identified seven single-nucleotide polymorphisms (SNPs) significantly associated with breast size (p<5·10−8): rs7816345 near ZNF703, rs4849887 and (independently) rs17625845 flanking INHBB, rs12173570 near ESR1, rs7089814 in ZNF365, rs12371778 near PTHLH, and rs62314947 near AREG. Two of these seven SNPs are in linkage disequilibrium (LD) with SNPs associated with breast cancer (those near ESR1 and PTHLH), and a third (ZNF365) is near, but not in LD with, a breast cancer SNP. The other three loci (ZNF703, INHBB, and AREG) have strong links to breast cancer, estrogen regulation, and breast development.
Conclusions: These results provide insight into the genetic factors underlying normal breast development and show that some of these factors are shared with breast cancer.
...The relationship between breast size and cancer is not entirely clear. Two studies have found that, for lean women, larger breast size is associated with a higher risk of breast cancer [7, 8]. For example, Kusano et al. [7] found that among women with a BMI under 25, those with a cup size of D or larger had a 1.8 times higher risk of breast cancer than those with a cup size of A or smaller.
Genetic factors also play a role in breast cancer risk, with many genetic associations discovered to date. In contrast, there have been no genetic studies of breast size and only one GWAS of breast density [9]. Twin studies have shown that breast size is about 56% heritable, with only about a third of this heritability shared with the heritability of obesity [10]
- 10. Wade TD, Zhu G, Martin NG: "Body mass index and breast size in women: same or different genes?" https://www.researchgate.net/profile/Tracey_Wade2/publication/46576952_Body_Mass_Index_and_Breast_Size_in_Women_Same_or_Different_Genes/links/00b7d52fbf89094b60000000.pdf . Twin Res Hum Genet. 2010, 13: 450-454. 10.1375/twin.13.5.450.
...Subsets of participants also reported other phenotypes. As covariates in the analysis, we included the projections onto the first five principal components of genetic ancestry as well as age, bra band size (in inches), and indicator variables for breast augmentation surgery, breast reduction surgery, mastectomy, past pregnancy, and current pregnancy or breastfeeding. Out of the 16,175 participants, all but 3 reported age, over 15,000 reported bra band size, about 12,000 reported breast surgery status (augmentation, reduction, mastectomy, or none), about 6,000 reported if they had ever been pregnant, and 4,000 reported if they were currently pregnant or breastfeeding.
Band size was used as a covariate instead of BMI because while almost every participant reported band size, only about half reported BMI. Band size has previously been used as a proxy for BMI in breast size research [8]. The correlation between BMI and band size in our sample was over 0.5. Furthermore, although bra size is easy to report, it is not a perfect proxy for actual breast volume. There is evidence that controlling for bra band size improves the correlation between cup size and breast volume [19].
...Bra size was coded from 0 to 9, corresponding to the categories: Smaller than AAA, AAA, AA, A, B, C, D, DD, DDD, and Larger than DDD, respectively. Mean size was 4.99 (just under a “C” cup) and the standard deviation was 1.45.
...On average, those reporting augmentation reported 0.5 size smaller breasts, reduction 1 size bigger, mastectomy 0.5 size smaller, and ever pregnant 0.1 size bigger. For every inch of band size, cup size was reported to be 0.1 sizes bigger on average
....There is a strong relationship in our data between BMI and breast size—each additional BMI unit corresponds to an increase of about 0.1 cup sizes on average. However, the SNPs in Table 1 are not in LD with any variants previously associated with BMI [35]; this is expected due to the inclusion of bra band size (which is correlated with BMI) as a covariate. Furthermore, even if we did not control for BMI, the strongest associations with BMI (e.g., rs1558902 near FTO) have effects of about 0.4 BMI units per allele. This would correspond to an expected βof about 0.04 for breast size for these SNPs, which is below the effect sizes we are powered to detect here. Indeed, if bra band size is not included as a covariate, rs1558902 has an estimated β of 0.07 (95% CI: 0.04 – 0.10) for breast size and p-value of 8·10−6as compared to βof 0.04 (95% CI: 0.01 – 0.07) with bra band size included.
The covariates included in the analysis explain about 9.7% of the variance in breast size in our data; including the 7 SNPs in Table 1 that are genome-wide significant increases this to 10.9%. We used these 7 SNPs to compute a genetic propensity score for breast size by counting the number of alleles associated with larger size that each participant carried. The average cup size among women in the top 5% of this score (women carrying 9 or more of the 14 possible “large” alleles) was 0.83 cup sizes bigger (5.39 versus 4.56) than the average cup size among women in the bottom 5% of this score (women carrying 4 or fewer “large” alleles)."
[An interesting start but leaves out a lot of desirable results: no GCTA estimate, no polygenic score of variance explained by all SNPs, no genetic correlations with BMI or breast cancer.]
"Large-scale genotyping identifies a new locus at 22q13.2 associated with female breast size", Li et al 2013 https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4159740/
"The samples consisted of the Swedish KARMA, LIBRO-1 and SASBAC studies genotyped on iCOGS, a custom illumina iSelect genotyping array comprising of 211,155 single nucleotide polymorphisms (SNPs) designed for replication and fine mapping of common and rare variants with relevance to breast, ovary and prostate cancer. Breast size of each subject was ascertained by measuring total breast area (mm2) on a mammogram.
Results: We confirm genome-wide significant associations at 8p11.23 (rs10086016, P = 1.3 × 10−14) and report a new locus at 22q13 (rs5995871, P = 3.2 × 10−8). The latter region contains the MKL1 gene, which has been shown to impact endogenous estrogen-receptor α transcriptional activity and is recruited on estradiol-sensitive genes. We also replicated previous GWAS findings for breast size at four other loci.
To evaluate whether there is any genetic overlap between mammographic breast area and breast cancer risk, polygenic scores (based on mammographic breast area) were calculated according to the methods by Purcell et al. [22] to test the combined effect of multiple weak associations across the genome. The SASBAC data, which has screen film mammograms for both breast cancer cases and controls, were used. In order to identify polygenic effects due to independent SNPs in linkage equilibrium with one another, we performed the analysis using a pruned dataset (51,303 SNPs). Linkage equilibrium-based SNP pruning was performed using the --indep-pairwise function (window size in SNPs: 1,500; the number of SNPs to shift the window at each step: 150; r2 threshold: 0.2) in Plink [10]. KARMA, the study with the most number of samples (n=3,420) was used as a reference dataset for computing polygenic scores. Ten sets of SNPs were generated from the mammographic breast area association results at Pvalue thresholds of 0.0001, 0.001, 0.01, 0.05, 0.1, 0.2, 0.3, 0.4, 0.5 and 1.0. Each subject was then scored using the sum of the number of reference alleles multiplied by the corresponding beta estimate from the mammographic breast area GWAS for the alleles in each of the SNP sets. Logistic regression was used compare the polygenic scores between breast cancer cases and controls. All models were adjusted for age at mammogram and BMI.
Estimation of the phenotypic variance explained by common variants for 1,206 subjects genotyped on both the iCOGS and Illumina HumanHap300 BeadChip was performed using the REML method described in Yang et al [23]. The estimate of variance explained for breast cancer was transformed from the observed scale to that on the underlying scale based on a specified prevalence rate of 0.0189.
Breast size was ascertained as the breast area on a mammogram in mm2. Mammograms of the cranial-caudal view in the KARMA and LIBRO-1 studies were automatically thresholded to find the breast edge and measured using ImageJ (Supplementary Figures 1 and 2). Mammograms of the medio-lateral oblique view in the SASBAC study were manually outlined by one reader to delineate the breast edge and exclude the pectoral muscle being before measured using Cumulus (Supplementary Figure 3).
Table 1: mean(SD) breast sizes/area/cross-section in cm^2:
n=3420 137.2 (58.0)
n=2243 124.4 (43.3)
n=1506 171.6 (54.3)
[rough means: 140(52.6)]
Only two SNPs showed genome-wide significant associations and consistent evidence of replication across all 3 datasets (rs10086016, P = 1.3 × 10−14, beta=-0.16; I2= 0; Phet=0.54 and rs5995871, P=3.2 × 10−8, beta=-0.13; I2= 0; Phet=0.94, Table 2) under the additive model.
...We also identified a novel locus at 22q13.2 (rs5995871, genotyped SNP with smallest Pvalue) which reached genome-wide significance at P = 3.2 × 10−8, mapping within MKL1. Imputation of 1KGP SNPs yielded multiple variants associated with total mammographic breast area, with the lowest P-value observed at rs73169028 (P= 1.22 × 10-8). This SNP was in high LD with rs5995871 (R-sq=0.833; D′=0.913). In conditional regression analyses, rs5995871 was sufficient to account for all association signals within the locus (±500 kb, Supplementary Figure 5). No heterogeneity in the beta estimates was observed for either locus across all three studies. A list of all genotyped SNPs which passed the suggestive threshold of P<1 × 10-5 is given in Supplementary Table 2. Five other SNPS (rs4849887 and rs17625845 near INHBB, rs12173570 near ESR1, rs7089814 in ZNF365, rs12371778 near PTHLH) that have previously been reported to be associated with bra size were also found to be associated with total mammographic breast area in our study at P<0.05 (Supplementary Table 3).
...Allele frequency differences by breast size were observed among both European and Asian populations for the top hits in the 8p11.23 and 22q13.2 regions. Every additional copy of rs10086016(C) and rs5995871(G) was associated with smaller total mammographic breast area. The frequencies of these alleles were both lower for the European CEU population (each ∼12%), than for the Asian CHB and JPT populations on HapMap (ranging between 24.5% to 38.6%) (Supplementary Table 4)...It is possible that the allele frequency differences for the top hits in both the 8p11.23 and 22q13.2 regions are linked to ethnic differences in breast size. Asian women tend to have smaller breasts on average when compared to Caucasian women [31]. In this study, we observed that the effect alleles of the two common variants which were found to be associated with smaller total mammographic breast area to be more common amongst the Chinese and Japanese HapMap populations compared to Europeans. However, it should be noted that since these SNPs explain only about 1% of the variance for breast size, a relatively slight difference in allelic frequency may explain only a small fraction of the actual phenotype.
...Given that there is a public interest in knowing whether there is a link between breast size and breast cancer, we examined whether breast cancer susceptibility loci were associated with mammographic breast size. In the landmark breast cancer large-scale genotyping association analysis involving more than 100,000 women conducted by the Breast Cancer Association Consortium (BCAC), 67 known and novel breast cancer susceptibility loci were reported [9]. Of the 13 breast cancer susceptibility loci associated (at P<0.05) with mammographic breast area only six SNPs showed a consistent (the allele associated with large size being also associated with breast cancer risk) direction of association (Table 3 and Supplementary Table 5). In a lookup of our top genotyped SNPs for total mammographic breast area in the consortium data, rs10086016(C) and rs5995871(G) were found to be associated with overall breast cancer risk (odds ratio [95% confidence interval]) of 0.95 (0.93 to 0.97) and 1.12 (1.09 to 1.15), respectively. Both SNPs were associated with a decrease in total mammographic breast area. Whilst polygenic scores derived from the “top” SNPs for association with total mammographic breast area in the KARMA dataset were found to be significantly associated with the same trait in the SASBAC dataset for Pvalue thresholds between 0.1 and 1 (P<0.05, Supplementary Figure 6), the smallest pvalue for association with breast cancer risk in the same dataset was 0.14.
...We also evaluated the proportion of phenotypic variance that could possibly be explained by all SNPs present on the current genotyping array used. For a subset of the SASBAC study (n=1,206), we had genetic data generated from both the customized iCOGS chip and the commercial Infinium HumanHap300 BeadChip. We estimated the proportion of phenotypic variance for mammographic breast area explained by all SNPs on each chip to be 0.31 (iCOGS, SE=0.16) and 0.47 (Illumina, SE=0.25), respectively (Supplementary Table 6). For breast cancer, the estimated proportion of phenotypic variance explained were 0.57 (iCOGS, SE=0.11) and 0.32 (Illumina, SE=0.17), respectively.
...Study findings on a potential link between breast size and breast cancer are mixed. Some studies have found that larger breast sizes are associated with increased risk of cancer, while others have found no link between breast size and cancer risk [32-35]. We expanded the analysis carried out by Eriksson et al. [5] to include 67 novel and known breast cancer susceptibility SNPs reported in a landmark paper on a mega-consortium effort (COGS) to identify breast cancer susceptibility variants [9] and found 13 breast cancer SNPs to be associated with breast size at P<0.05, suggesting that there is a significant overlap among SNPs for breast size and breast cancer risk (P=2.91 × 10-7 in a two-tailed test of population proportion where the alternate hypothesis is that the true proportion is not equal to 5% as expected by chance). It is however, notable that the effects of 6 of the 13 SNPs were in opposite directions for breast size and breast cancer risk. Although we have found evidence that there is a connection between genetic determinants of breast size and breast cancer risk, our results show that larger breast size are not necessarily associated with an increase breast cancer risk. On the iCOGS chip which has been customized to study genetic variants predisposing to breast cancer, we also saw no evidence of a shared polygenic component between mammographic breast area and the disease, suggesting that caution should be exercised when interpreting any positive correlation between these two phenotypes."
[If these GCTAs are right, breast size is almost entirely additive: the twin study was ~0.5, the better GCTA is also almost ~0.5. The estimated effect sizes are also quite large: the top alleles account for a tenth of cup size each, indicating that are likely not that many variants involved. If so, it should respond to any selection for larger breasts very quickly, yet hasn't. The racial differences on both the phenotype and genetic levels also suggests selection for different levels in different places. Larger breasts, aside from the breast cancer issue which shouldn't affect reproductive fitness too much historically (especially compared to child birth mortality), seem like they would come with penalties: more back pain, less athleticism, added metabolic expense of the additional ounces of flesh, more resources while growing. Differing intensity of sexual selection might explain why more or less expensive secondary sex characteristics?
At a narrow-sense SNP heritability of 0.47 and population mean of breast size area 140(52.6) cm^2, upper bounds on the efficacy of selection are 39cm^2 with 10 embryos and 26cm^2 with a more realistic 4:
embryoScores <- function(n, variance) { rnorm(n, mean=0, sd=sqrt(variance*0.5)); }
embryoSelectionGain <- function(n, variance) { scores <- embryoScores(n, variance)
return(max(scores) - mean(scores)); }
simEmbryoSelection <- function(n=2, variance=0.47, iters=100000) { replicate(iters, embryoSelectionGain(n, variance)); }
mean(simEmbryoSelection(n=10))
# [1] 0.7469298563
mean(simEmbryoSelection(n=10)) * 52.6
# [1] 39.28784006
mean(simEmbryoSelection(n=4)) * 52.6
# [1] 26.25772435
23andMe paper: top 7 SNPs have an incremental variance explained of 10.9% - 9.7% = 1.2%, so:
mean(simEmbryoSelection(n=4, variance=0.012)) * 52.6
[1] 4.193488721
Li et al 2013 doesn't report the variance explained by their polygenic scores in the paper or supplemental material, but as their sample is half the size of the 23andMe sample, and they only report 1 new genome-wide statistically-significant hit, we could guess that their polygenic score meta-analyzed with the 23andMe polygenic score would only increase it by half, to 1.8%:
R> mean(simEmbryoSelection(n=4, variance=0.018))
[1] 0.09767069559
R> 0.09767069559 * 52.6
[1] 5.137478588
R> 0.09767069559 * 1.45
[1] 0.1416225086
So we could expect a 0.097SD increase in cup size or area in cm^2.
What value is that? We can extrapolate from beast augmentation (https://en.wikipedia.org/wiki/Breast_augmentation): if many women are willing to pay thousands of dollars for plastic surgery, despite the unpleasantness of surgery, the risk of complications, the chance of the implants bursting within a few years and needing to be monitored and eventually surgically removed or replaced, the potential social stigma, and the willingness to take such a measure in the first place, then the value to them must be extremely high, as indicated by post-operative increases in self-esteem and libido (https://en.wikipedia.org/wiki/Breast_augmentation#Mental_health).
And many find it worthwhile; as one of the most popular cosmetic surgeries (second most popular in 2015 after liposuction http://www.surgery.org/media/news-releases/american-society-for-aesthetic-plastic-surgery-reports-more-than-135-billion-spent-for-the-first-time-ever, 305856 procedures done costing \$1,191,025,070, average $3,497/$3,964 http://www.surgery.org/sites/default/files/ASAPS-Stats2015.pdf) ), perhaps as many as 4% of all American women have had breast augmentation surgery (https://fivethirtyeight.com/datalab/dear-mona-what-percentage-of-women-have-breast-implants/).
So if 4% of women are willing to pay ~$3750 for breast augmentation surgery, and we assume that the value to the rest is exactly $0 (to be conservative, although we can imagine that many women would be happy if they woke up with larger breasts), then the expected loss of the surgery is 0.04*3750=$150 and so the value must be >$150.
How much does the surgery increase cup size or area in cm^2 on average?
Hard sources are scarce and the target cup size or CC volume of an implant will differ based on each woman's desires, body size, breast shape, etc; but reading through plastic surgeon websites and discussions, it seems that ~100-300 CC yielding an increase of 1-2 cups is the common target and no larger.
If 1 cup is worth >$150, then one would expect a genetic gain of 0.14 cups to be worth 0.14*150>$21 in future gains.
The reported mean age of breast augmentation surgery users is 34, so arguably we should discount that >$21 by 34 years to compare to the present-day cost of embryo selection, so its net present value would be >21 / (1 + 0.05)^34 = >$4 (using my usual 5% discount rate). On the other hand, the value of larger breasts also arguably starts in puberty, and American girls begin puberty ~9.5yo in 2013 (http://www.reuters.com/article/us-girls-puberty-idUSBRE9A304D20131104), in which case it'd be more like >$13.
What factors have I left out? The main ones seem to be the possible increase in breast cancer, and the definite increase in BMI.
The minimal increase in breast cancer in Li et al 2013 seems to somewhat contradict Eriksson et al 2012's results, and indicates no net effect.
Wade et al 2010 finds that https://www.researchgate.net/profile/Tracey_Wade2/publication/46576952_Body_Mass_Index_and_Breast_Size_in_Women_Same_or_Different_Genes/links/00b7d52fbf89094b60000000.pdf
> the AE model gave the best fit and the proportions of variance explained by the latent sources of A and E are shown in Figure 2. It can be seen that only 15% of the variance of bra cup size is due to the additive genetic sources contributing to BMI with a further 41% of genetic variance specific to BRA. The correlation between genetic sources contributing to BMI and bra cup was 0.52 and the correlation for non-shared environmental sources was 0.44
15.1/40.8=0.37, so I believe that for every 1 SD we increase bra size by selection (without any selection against BMI), we should expect to increase BMI by 0.37SD.
So if we can increase bra size by 0.097SD, then we would also wind up increasing BMI by 0.00359 SD.
In my embryo selection essay, I used http://vinecon.ucdavis.edu/publications/cwe1201.pdf "The Marginal External Cost of Obesity in the United States", Parks et al 2012 to estimate the cost of 1 SD of BMI at$3586; so the cost of the BMI increase is $128.
The good news is that BMI polygenic scores work much better than breast polygenic scores, with the highest one at 15.3%. So we can more than undo the effect of breast selection on BMI:
R> mean(simEmbryoSelection(n=4, variance=0.153))
[1] 0.2845980551
R> mean(simEmbryoSelection(n=4, variance=0.153)) * 3586
[1] 1020.913556
However, that doesn't necessarily mean we want to do any selection on breast at all: the cost in BMI may be too high. We can undo that 0.00359SD of BMI increase but maybe it's worth more if we selected on BMI alone?
We can say that the cost of the BMI increase is $128, and I already estimated the breast value at >$21; but the lower bound is not tight. It could easily exceed $128, in which case we do want to do selection on both traits.
On the other hand, there remains the issue of breast cancer, one could plausibly argue that the cost of BMI may keep going up over time, that larger breasts may or may not be helpful but always have drawbacks like back pain and less athleticism, from a sexual attractiveness point of view slenderness is more reliably & universally appealing, and that if one is going to do embryo selection for attractiveness at all, it would probably be better to select for height, lower BMI, and hair/eye color.
True, it costs next to nothing to incorporate breast size as a trait in an existing embryo selection (since the SNP array will doubtless have most of the relevant SNPs on it), but the genetic correlation with BMI makes it a questionable thing to select on, especially compared to something like IQ where almost all of the genetic correlations are in desirable directions and so it's underestimated if anything.
On net, selection for breast size probably isn't a good idea at this point without stronger polygenic scores for BMI.
