Researchers have mapped out some of the mechanisms that may affect women’s fertility from the teenage years to menopause.
These mechanisms largely depend on naturally occurring chromosome errors – errors that vary depending on age group.
This is the conclusion by an international research group in a new study, led by researchers from the University of Copenhagen.
The scientists, who come from a number of European universities, have reached their conclusion after examining 3000 egg cells from girls and women between the ages of nine and 43.
‘We have known for a long time that we humans have a unique fertility curve compared to many other species.
The curve starts out very poorly in the teenage years and starts to go downhill again when women reach their 30s.
But until now, we have not known what is actually causing these changes’, says Head of Research and Professor Eva Hoffmann from the Department of Cellular and Molecular Medicine at the University of Copenhagen.
Unlike men who do not form sperm until they reach puberty, women are born with all the egg cells they will have available throughout life.
However, the eggs are immature and do not fully develop until the menstrual cycle begins.
‘While the eggs lie dormant, a kind of molecular glue will make the chromosomes stick together. Later, when the eggs are maturing, the chromosomes divide.
But the older the women become, the greater the risk that the glue will break down prematurely’, says Eva Hoffmann.
The hereditary material thus falls apart, resulting in chromosome errors which may, for example, lead to syndromes such as Down, Turner or Kleinfelter. Or which may make the eggs infertile.
Also in teenage girls, the researchers found a greater incidence of chromosome errors during the maturing of the eggs. In this case mostly due to the eggs not reaching a sufficient level of maturity.
This meant that in adolescence, especially the larger chromosomes in the hereditary material developed defects – and thus increased the likelihood that the eggs would be expelled by the body without being fertilized.
As the teens turned into young women, the researchers observed how the eggs became healthier, while the chromosome errors gradually disappeared. A trend that continued until the women were in their late 20s, after which other types of chromosome errors started to set in.
Wider Hips and Grandmothers
Scientists do not yet know for sure exactly why human fertility rises, peaks and falls within a defined age range.
By comparison, our close fellow species, the chimpanzees, do not in the same way experience menopause, but are rather consistently fertile throughout their adult life.
This is one of the 3000 human egg cells from the Hoffmann Group’s study. The image is credited to Department of Cellular and Molecular Medicine, University of Copenhagen.
According to Eva Hoffmann, it may be a matter of two evolutionarily developed mechanisms in humans.
First, a mechanism that protects very young women from becoming pregnant until their bodies are fully developed – and thus better able to bear children due to, for example, wider hips that reduce the risks associated with giving birth.
Second, a mechanism that potentially makes older women take on a new, supportive role as grandmothers when their own children become able to produce offspring – a theory which within a number of research fields has become known as the ‘grandmother hypothesis’.
Eva Hoffmann points out that the new results may be used to improve the dissemination of information about child-bearing and pregnancy loss. Just as the increased knowledge may be able to improve the treatment of infertility in the long term.
‘Pregnancy loss is still a taboo, but with knowledge like this, we are able to better understand and demonstrate that it is a natural thing.
At the same time, a greater understanding of the mechanisms behind our biological clock may enable us to better control the breakdown of the eggs. Either in the eggs themselves or in the maturation process in the fertility clinic’, says Eva Hoffmann.
Female fertility, and the factors that regulate fertility and number of children born are of broad general interest because of their implications for health, population size and ageing. Reproductive life span from the onset of puberty, age-specific fertility rates, and twinning frequency all contribute to fertility.1–4
Other factors influencing female fertility include developmental programming, common diseases such as polycystic ovarian syndrome (PCOS) and endometriosis, and the cumulative effects of environmental exposures and lifestyle.5–8
This genetic contribution to reproductive traits and diseases can result from rare mutations in specific genes and common variation at many sites in the genome each with small effects. In the last decade, genome-wide association studies (GWAS) have transformed our understanding of genetic contributions to these complex traits and diseases.13
The results of these studies have led to discovery of novel genes and pathways influencing specific traits and diseases, new discoveries in disease epidemiology, and the discovery or repurposing of candidate therapeutics.13
Results for GWAS studies for reproductive traits (Fig. (Fig.1)1) demonstrate how increases in sample size over time have improved the power of these studies to identity the many genetic factors with small effects contributing to variation in reproductive lifespan and disease.
Studies on genetic contributions to fertility are taking place during a period of considerable demographic change with a substantial fall in age at menarche and a tendency for women to delay childbearing in many countries.
This delay in childbearing is associated with an increase in age at first birth, a decrease in the fertility rate because of age-specific effects,14 and an increase in the dizygotic twinning rate.15,16
Detailed investigation of the genetic basis of the female fertility is providing crucial information for understanding variation in female fertility and preventing or treating disorders that contribute to reduced fertility.
This review aims to describe the complexity involved with genetics of female fertility and highlight the important observations emerging from the genetic studies investigating reproductive lifespan, fertility traits, menstrual disorders, and the pathophysiology of disease.
Genetics of reproductive lifespan
Reproductive lifespan in women is defined as the time from the onset of puberty until the menopause when the pool of oocytes is depleted and menstrual cycles cease.11 Primordial follicles develop during gestation and the maximum oocyte pool at birth then declines until exhausted at the time of the menopause, associated with declining fertility and increased twinning rates with age (Fig. (Fig.2).2).
The health outcomes from variation in timing of both age at menarche and natural menopause include effects on fertility, cardiovascular disorders, hypertension, glucose intolerance, osteoporosis, obesity, breast cancer, ovarian cancer and endometrial cancer.11,17 However, the underlying mechanisms explaining the association of age at menarche and menopause with many of these long-term health impacts are yet to be identified.
Menarche occurs with maturation of the reproductive endocrine system and denotes the onset of menstrual cycles and sexual maturity for women. It usually occurs between 9 and 14 years of age. The average age at menarche has declined over the last century in high income countries including Europe and North America.22 Early menarche is associated with early initiation of sexual activity, early pregnancy, high risk of sexually transmitted infections, increased risk for obesity, type 2 diabetes (T2D), breast cancer and cardio metabolic disease.23–28 At the other end of the distribution, delayed puberty is associated with short stature and lower bone mineral density.29
The timing of puberty varies between individuals and is a highly polygenic trait with both rare and common variants contributing to the variation in age at menarche (AAM). Rare mutations in genes that disrupt the development and function of the gonadotrophin-releasing hormone (GnRH) pathway, pituitary hormones, and their receptors can result in idiopathic hypogonadotropic hypogonadism (IHH) and the absence of puberty.11,30 These include mutations in genes for kisspeptin (KISS1), GnRH (GNRH1), follicle-stimulating hormone (FSH), luteinizing hormone (LH) and their respective receptors. Some rare mutations for IHH have been implicated in less severe delayed puberty and may contribute to the population variability in AAM.11 In contrast, activating mutations in KISS1 and kisspeptin receptor (KISS1R), and paternally inherited mutations in two imprinted genes Makorin ring-finger 3 (MKRN3) and Delta-like 1 homologue (DLK1) can result in central precocious puberty (CPP).31,32 MKRN3 is an intronless gene located on the long arm of chromosome 15 in a cluster of imprinted genes in the region associated with Prader–Willi syndrome.31 MKRN3 is expressed from the paternal allele (maternally imprinted) in the arcuate nucleus and inhibits the secretion of GnRH during the prepubertal period in childhood.33 Mutations associated with CPP31 include a four-base deletion in the proximal promoter of MKRN3 identified in a girl with non-familial idiopathic CPP who exhibited pubertal development around the age of seven.34 The deletion was associated with reduced promoter activity in vitro.34 DLK1 is located on chromosome 14 and encodes a transmembrane protein with multiple epidermal growth factor repeats. Like MKRN3, DLK1 is expressed from the paternal allele and paternal inheritance of a complex genomic rearrangement including the translation start site of DLK1 was associated with isolated familial CPP.32 The association of CPP with loss-of-function alleles in two paternally expressed genes supports a role for imprinting affecting the timing of puberty.32
GWAS of AAM in healthy women in European and Non-European populations have identified key genetic factors regulating puberty timing as reviewed previously.11,29,30 The Lin-28 Homologue 28 (LIN28B) at 6q21 was the first of the many loci identified from five independent GWAS for AAM.35 The most recent GWAS conducted in ∼370,000 women of European ancestry identified 389 independent signals explaining ∼7.4% of the population variance in age at menarche (Fig. (Fig.1),1), corresponding to ∼25% of the estimated heritability.36 Eight of the lead SNPs from the GWAS results were non-synonymous variants altering expected protein sequences and lead SNPs were highly correlated with non-synonymous variants implicating a further 24 genes.36 These included aromatase (CYP2C19A1), and genes disrupted in rare disorders of puberty GNRH1 and KISS1.36 Analyses of the data sets for genetic effects on gene expression demonstrated positive enrichment for AAM-associated variants in five central nervous system tissues, notably the pituitary gland and hypothalamus36 supporting an important role of central mechanisms in reactivation of the hypothalamic pituitary axis and onset of puberty. Expression of 205 genes in these tissues were regulated by AAM-associated variants including higher expression of LIN28B in the pituitary gland associated with later AAM.36 Formal analysis of overlap in signals for AAM and genetic effects on gene expression in blood (expression quantitative trait loci; eQTLs) identified evidence for causal or pleotropic effects for 60 regions36 with the variant(s) associated with AAM driving variation of a specific genes in each region.
In Japanese women, the mean age at menarche was 13.9 years with a strong secular trend for decreasing age at menarche to a mean age of 12.3 years for women born after 1965.37 GWAS in 67,029 women identified 10 significant association signals for age AAM, including signals in two novel regions not reported previously in European women and one novel Japanese-specific signal in a previously reported region near PTPRD. More variants had larger effects on early, compared with late menarche timing, consistent with evidence in European studies.37
Menopause is defined as the permanent cessation of menstruation resulting from the loss of follicular activity. Menopause generally occurs between ages of 40–60 years with the average age of ~51 years in western countries.38 The age at menopause (ANM) has a strong genetic component with more than 50% of variation due to genetic factors.39 A genomic analysis for age at natural menopause was conducted in ~70,000 women (Fig. (Fig.1)1) to identify both common and low-frequency variants contributing to genetic variation.40 In the analysis of common variants, 54 independent signals were identified in 44 genomic regions (P < 5 × 10−8) with a range of effect sizes from 0.07 to 0.88 years per allele. Exome array analysis identified genome-wide significant evidence for association with two correlated low-frequency missense variants in DNA helicase B (HELB). Although interpretation of the GWAS results have limitations because specific target genes in each region are yet to be determined, the results implicate a substantial role for DNA damage repair in reproductive ageing40 including repair of double strand breaks, mismatch repair and base-excision repair. Pathway analysis also suggested enrichment for a set of genes associated with POI, including MCM8, POLG and MSH5.40
The risk loci for age at menopause identified in European populations have also been studied in women with different ethnic origins. Out of 22 SNPs identified in European populations, 8 SNPs were reported to be significantly associated with age at menopause in a Chinese population confirming risk SNPs in NLRP11, TMEM150B and BRSK1.41 A recent GWAS study for ANM in 43,861 Japanese women identified 16 independent genome-wide significant signals (Fig. (Fig.1),1), of which 8 were novel and not previously reported in Europeans.37 Of the remaining 44 significant SNPs reported in European populations and polymorphic in the Japanese population, all had a consistent direction of effect and about half were associated with ANM at nominal levels of significance. Four of the novel signals were highly correlated with missense variants and implicate the genes GNRH1, HMCES, ZCCHC2 and ZNF518A in the regulation of menopause timing.37 The signal in GNRH1 is the same predicted deleterious missense variant reported for ANM in Europeans.37
In African American women, only one of 37 SNPs chosen for replication for age at menarche and none of 16 SNPs for age at natural menopause replicated in the Women’s Circle of Health Study.9 No variants met the generally accepted threshold for genome-wide significance. Larger studies will be required to determine whether lack of replication is due to differences in genetic architecture or mechanisms regulating reproductive lifespan in African American women.
Potential health impacts and links with other health disorders
Variation in AAM and ANM have wide-ranging effects on human health. In a study in the UK Biobank, age at menarche was associated with 26 adverse health outcomes.14 Earlier AAM is associated with higher risks for type 2 diabetes (T2D), cardiovascular disease, and effects on gynaecological, gastrointestinal, musculoskeletal, and respiratory conditions.14 The relationships are complex with non-linear relationships between AAM and T2D and cardiovascular disease.11,14,42 Early menarche increases risk for both T2D and cardiovascular disease while later menarche also increases risk for cardiovascular disease, but is neutral for T2D.11 BMI also plays a role for many of the same health outcomes. Following adjustment for body composition and socio-economic status, associations with early menarche remained significant for 14 health outcomes and associations with late menarche were significant for eight health outcomes.14 Early menarche was associated with higher risks for uterine fibroids, endometriosis and earlier natural menopause.
Later age at menopause is associated with increased risks for breast, ovarian and endometrial cancer. Many of the genetic markers influencing menopause are related to DNA damage repair genes including BRCA1, MSH6 and CHEK2 that also predispose to familial cancers.39 In addition, later age at menopause results in longer exposes to high levels of oestrogen for women. Poor DNA damage response that increases cancer risk might be expected to lead to earlier menopause, opposite to the evidence from epidemiological studies. Using the available genetic data from studies for breast cancer and age at menarche, predicted age at menopause from genetic variants showed increased risks of breast cancer with later age at menopause40 and the effects were greater in oestrogen receptor positive breast cancer. Genetic variants associated with DNA damage repair genes had smaller effects than other markers.40 Taken together, the results suggest that increased exposure to oestrogen with increased reproductive lifespan is the predominant effect on risk for breast cancer.
Diseases influencing fertility
Polycystic ovary syndrome
Polycystic ovary syndrome (PCOS) is a complex, hormonal and metabolic disorder affecting 5–20% of women of reproductive age globally and characterised by hyperandrogenism, ovulatory dysfunction, polycystic ovarian morphology and gonadotropic abnormalities.62,63 PCOS is the most common cause of infertility64 and also increases the risk for type 2 diabetes, gestational diabetes, venous thromboembolism, cerebrovascular and cardiovascular disease and endometrial adenocarcinoma.65 The aetiology of PCOS remains unclear with diagnostic criteria proposed for PCOS66 including the National Institutes of Health (NIH), Rotterdam and Androgen Excess Society (AES) criteria. Familial aggregation and twin studies suggest genetic factors play a strong role in pathogenesis of PCOS with heritability estimates of 70%.65,66
The first GWAS conducted in Chinese patients in 2011 (Fig. (Fig.1)1) identified three genomic regions associated with the disease.67 Additional studies66,68,69 identify 16 independent signals in 15 genomic regions associated with PCOS including signals near important reproductive hormone genes FSHR, LHCGR and FSHB.70 The signals also include variants in or near three epidermal growth factor genes and genes associated with diabetes.40,70 As with similar studies in other reproductive diseases, the total heritability explained by GWAS identified PCOS risk SNPs is relatively low (<10%).65
Mendelian randomisation is an analytical method using genetic variation to investigate the likely causal relationship between an exposure trait (or risk factor) and a health outcome. Genetic variants are inherited independently and fixed at birth and subject to less confounding than other measured risk factors. Increasing evidence of association between genetic variants and many common traits means Mendelian randomisation models can use genetic variants associated with a risk factor to infer relationships with a health outcome. The models assume the genetic variants used have strong evidence for association with the risk factor and do not influence the outcome through other unrelated biological pathways. In PCOS studies, Mendelian randomisation demonstrated causal roles for higher BMI, greater insulin resistance and reduced sex hormone binding globulin concentrations in serum.68 The causal role of PCOS risk SNPs for higher BMI, higher insulin resistance, and lower levels of sex hormone binding globulin (SHBG) has direct clinical applications for planning lifestyle modification as a prevention strategy and inclusion of metformin in treatment plans for PCOS.68 Discovery of additional genetic factors and further characterisation of the signals identified will provide greater insight into the pathogenesis of the complex phenotypes in PCOS.
Endometriosis is a complex disease characterised by ectopic lesions of tissue resembling endometrium in the peritoneal cavity.7 The disease affects 7–10% of women and is associated with pain and infertility. Early twin studies identified evidence for genetic effects on the liability for hysterectomy,71 one of the most commonly performed surgical procedures for women. Major indications for hysterectomies in reproductive age women are endometriosis (30%) and uterine leiomyomas (>50%).72,73 Subsequent studies in twins on genetic influences on the liability for endometriosis estimated the heritability at ~50%.74,75
Genomic regions and genes associated with endometriosis risk are reviewed in detail elsewhere.76–78 The most recent meta-analysis (Fig. (Fig.1)1) identified 14 genomic regions associated with disease risk.79 Endometriosis is an oestrogen-dependent disease and Oestrogen receptor 1 (ESR1) is the predominant receptor for oestrogen action in the endometrium.80 Genomic signals associated with endometriosis include regions flanking the gene for ESR1, signals upstream of follicle-stimulating hormone beta subunit (FSHB) known to increase FSH concentrations,79 and near the oestrogen-regulated and early response gene (GREB1) first identified in breast cancer cell lines and tumours.81 Other regions include candidate genes with roles in cell migration, adhesion and proliferation including Cell Division Cycle 42 (CDC42), Cyclin-Dependent Kinase Inhibitor 2B Antisense (CDKN2B-AS1) and Kinase insert domain receptor (KDR).82–84
Mechanisms leading to formation of lesions are poorly understand, but one source for cells initiating these lesions is thought to be cells shed from the endometrium and deposited in the pelvic cavity through retrograde menstruation.7,76,85 On chromosome 1, studies on genetic regulation of gene expression in blood86 and endometrium78,86 show the critical SNPs in this region influence expression of both the long non-coding RNA LINC00339 and CDC42. There are chromatin interactions between risk SNPs and gene promoters for both LINC00339 and CDC42.86 Luciferase reporter assays support the effect of genetic differences on the interaction between the regulatory element and the promoter of CDC42.86 Formal analysis of the overlap of signals for endometriosis risk and genetic effects on gene expression provides strong evidence that key SNPs associated with endometriosis on chromosome 1 and chromosome 12 regulate LINC00339 and vezatin VEZT expression, respectively.78,87
Overlap in genetic contributions to different traits and diseases
The hypothalamic/pituitary/ovarian axis plays a central role in development and function of many reproductive processes. It is perhaps not surprising that variation affecting key genes in this pathway influence multiple diseases and traits. A notable example is SNPs upstream of the transcription start site of FSHB. SNPs in this region are associated with increased concentrations of circulating FSH,88 decreased concentrations of LH,88 shorter menstrual cycles,89 increased dizygotic twinning,54 decreased risk of PCOS,69 increased endometriosis risk,95 and earlier menopause96 (Fig. (Fig.4).4). It remains to be determined if the association signals for all these traits act through the same causal SNPs and functional mechanisms. In the study on FSH and LH concentrations, the genetic signals had opposite effects on hormonal concentrations despite positive overall correlations in FSH and LH concentrations supporting complex relationships in the regulation of FSH and LH. Other associations support common mechanisms since higher FSH concentrations at the time of follicle selection are associated with increased DZ twinning44 and shorter menstrual cycles are associated with higher endometriosis risk.90
Potential overlap for other traits includes genes influencing both DZ twinning and POI and endometriosis and ovarian cancer. There is a small, but significant increase in mothers of DZ twins reaching menopause before the age of 40 compared with mothers of MZ twins.91 Low-frequency variants in GDF9 play a role in both DZ twinning and POI, including at least one GDF9 variant influencing twinning and seen in a patient with POI.55 Genomic loci with common variants influencing age at natural menopause are located close to genes known to carry rare mutations causing hypogonadotropic hypogonadism (CHD7, FGFR1, SOX10, KISS1R, and TAC3) and genes associated with POI.40 Further research will help to understand the relationships between ovarian development, disorders of puberty, DZ twinning, POI, and age at natural menopause.
Understanding the functional consequences of genetic association for the same signals in different traits will provide important insights into the similarities and differences in gene regulation underlying risk for the different diseases. The genetic locus associated with endometriosis risk on chromosome 1p36 (discussed above) overlaps completely with an association signal for ovarian cancer.79,92 The association signals are located in WNT4.79,92 Subsequent follow-up functional studies show correlated association signals for endometriosis in this region regulate LINC00339 and CDC42 not WNT4,83 and one or both target genes may also play a role in ovarian cancer risk. There is genetic association near the oestrogen receptor 1 (ESR1) locus with four independent signals for endometriosis and five independent signals for breast cancer79,93 (Fig. (Fig.4).4). Analysis showed overlap for only one of the signals, in an intron of ESR1.79 Intronic variants in ESR1 are also associated with other reproductive traits, including age at first birth and number of children born.44 In agreement with limited overlap between signals for endometriosis and breast cancer in this region, signals for age at first birth and number of children born did not overlap with other disease associations for timing of puberty, breast cancer, breast size, or bone mineral density in the ESR1 region44 suggesting complex regulation of gene expression and disease outcomes at this locus.
In addition to discovery and overlap in effects for individual genes, GWAS data provides powerful approaches to understand shared genetic risk between traits and diseases. Genome-wide SNP genotype data from a discovery sample can be used to estimate the genetic variation due to common SNPs or SNP heritability, and to calculate a polygenic risk score for individuals in an independent sample.13,94 The Polygenic risk score (PRS) combines association results from genome-wide genotyping into a single estimate of the genetic risk for a disease or trait for each individual. The PRS score is calculated from the number of risk alleles carried, weighted by the effect size estimated from the discovery sample.13,94 It is often standardised to a mean of zero with a standard deviation of 1 for ease of interpretation.94 The risk scores are not very informative for individual prediction, but explain sufficient variation to determine individuals at highest or lowest risk in populations, and to understand genetic contributions to related traits.13 Where samples are fully independent, calculating genetic contributions to related traits provides a powerful design reducing issues of shared environment and ascertainment in epidemiological studies. Overlap between endometriosis and ovarian cancer extends beyond the observed overlap at the chromosome 1p36 locus discussed above. Observations from epidemiological studies can be confounded due to diagnosis of endometriosis at laparoscopy close to a diagnosis of ovarian cancer. PRS analysis with genotype data from independent samples for endometriosis and ovarian cancer showed shared genetic risk between endometriosis and most histotypes of ovarian cancer95 suggesting some common molecular pathways for the two diseases including the overlap at chromosome 1p36. Prediction of individual risk is improving for some diseases with better estimates of the genetic risk factors. While not sufficiently predictive in isolation, risk scores may be used in combination with other clinical data for patient stratification. The application of risk prediction to inform breast cancer screening is being evaluated in the population based Women Informed to Screen Depending On Measures of risk (WISDOM) study.96
As noted earlier, there are significant additive genetic effects for age at first birth45,97 and number of children ever born.97 Results show a significant negative genetic correlation between number of children ever born and the age at first birth suggesting genes contributing to later first birth are associated with fewer children.97 These relationships are complex because environmental effects and demographic changes also play a role with women choosing to delay childbearing in many countries. Relationships between age at first birth and lifetime number of children are also associated with genetic effects on twinning. Mothers of twins tend to have an earlier age at first birth and raise more children to adulthood in favourable environments.98,99 Polygenic risk score analysis from the GWAS results for DZ twinning suggest genes contributing to DZ twinning may partly explain genetic effects on fertility. The polygenic risk score for DZ twinning was significantly associated with DZ twinning in an independent sample from Iceland.59 In this sample, the risk score for DZ twinning was associated with a higher likelihood of having children, earlier age at first birth, and greater number of children.59
Genetic studies can also inform complex relationships between reproductive traits and related health outcomes. A large-scale meta-analysis supported an association of early menarche and late menopause with increased risk of breast cancer and demonstrated that excess risk associated with advancing menarche by one year was higher than excess risk associated with lengthening menopause by one year.100 This epidemiological evidence is supported by the Mendelian randomisation analyses demonstrating the causal relationship between delayed natural menopause and increased breast cancer risk.40 Understanding these relationships is further complicated by effects of variation in body mass index (BMI). There is a strong inverse genetic correlation between AAM and BMI.36 Thirty-nine signals overlap between AAM and BMI, but most AAM signals make some contribution to adult BMI.36 Using information from different genetic studies allowed estimates of the direct effects of AAM on sex-steroid-sensitive cancers after adjusting for genetically predicted BMI. In these models, later AAM was associated with reduced risks for breast, ovarian and endometrial cancers.36 Analysis of cancer subtypes suggests effects were most strongly associated with oestrogen receptor positive breast cancer and serous ovarian cancer. The effects of earlier puberty timing on higher risks of the sex- steroid sensitive cancers might be related to longer duration of exposure to sex steroids and/or increased activity of the hypothalamic-pituitary axis associated with earlier puberty and reproductive traits including dizygotic twinning.
University of Copenhagen
Eva Hoffmann – University of Copenhagen
The image is credited to Department of Cellular and Molecular Medicine, University of Copenhagen.
Original Research: Closed access
“Chromosome errors in human eggs shape natural fertility over reproductive life span”. Eva Hoffmann et al.