Selection on fecundability requires heterogeneity. Demographers have recognised that fecundability varies across individuals since the earliest studies on fecundability and contraceptive efficacy (Gini, 1924/1977; Pearl, 1933; Potter, 1960; Sheps, 1964; Tietze, 1959). Substantial effort has been directed towards measuring fecundability when it is heterogeneous (Bongaarts, 1975; Dunson and Weinberg, 2000; Gini, 1924/1977; Heckman and Walker, 1990a, 1990b; Larsen and Vaupel, 1993; Majumdar and Sheps, 1970; Pearl, 1933; Potter, 1960; Sheps, 1964; Sheps and Menken, 1973; Suchindran and Lachenbruch, 1975; Weinberg and Gladen, 1986).

Prospective studies find substantial differences in fecundability across categories other than age, including education level (Boxem et al., 2025; Jørgensen et al., 2023; Schrager et al., 2020); health behaviours such as alcohol consumption (Fan et al., 2017), smoking (Wootton et al., 2023; Zhou et al., 1996), high caffeine consumption (Dunson, 2001) and dietary patterns (Cueto et al., 2022; Willis et al., 2020, 2022); and physical characteristics such as large or small body size (Loy et al., 2018; McKinnon et al., 2016; Wise et al., 2010, 2013; Wootton et al., 2023; Zhang et al., 2020), higher body mass index (Boxem et al., 2024), certain menstrual cycle traits (Pedersen et al., 2024; Wesselink et al., 2016; Zhang et al., 2017) and hypertension (Xiong et al., 2024). Likely as a result of heterogeneity itself, observed fecundability is 20–30% higher among women who have had a prior pregnancy or birth than it is among those of the same age who have not, with differences rising above 100% at later ages in some studies (Rothman et al., 2013; Steiner and Jukic, 2016; Wesselink et al., 2017).

Preconception cohort studies can provide both crude and adjusted age patterns in fecundability. Adjustment is especially necessary in contexts where the age pattern of childbearing is stratified by levels of advantage, since more advantaged populations tend to exhibit higher fecundability on average. Recent large high-quality preconception studies that have followed pregnancy seekers in North America (Wesselink et al., 2017) and Denmark (Rothman et al., 2013) have found that adjustments for behavioural factors and sociodemographic characteristics changed the estimated age pattern of fecundability, amplifying decline with age compared to crude estimates. Between the early twenties and the late thirties, crude fecundability declined by 25% in the North American study and was flat in the Danish study, while adjusted fecundability declined by 40% and 33% in the North American and Danish studies, respectively. These changes with adjustment illustrate the salience of social and life course processes in determining the ages at which contemporary individuals seek to conceive.

One way to avoid the selection problems in contemporary data is to use historical data from pre-demographic transition populations. By focusing on marital fertility among populations in which no fertility timing or limitation was practiced beyond prohibiting intercourse outside of marriage, demographers have sought to identify a variety of biological averages and maxima, including measures of fecundability by age (Eijkemans et al., 2014; Henry, 1961; Larsen and Yan, 2000; Leridon, 2008; Leridon and Menken, 1979; Menken et al., 1986; Menken and Larsen, 1986; Ridley et al., 1969).

A summary of these contributions to age patterns of reproductive capacity and a discussion of their implications for contemporary individuals were provided by Menken and colleagues in the mid-1980s (Menken, 1985; Menken et al., 1986). While they could not measure fecundability directly (because pregnancy loss is not well measured in historical or contemporary vital statistics), the historical data still provide insights into its age pattern. The historical age pattern of effective fecundability offers an upper bound, since as long as the probability of pregnancy loss does not decline with age, effective fecundability declines with age by at least as much as fecundability itself declines. The historical evidence reviewed by Menken and colleagues indicates that effective fecundability was approximately stable until age 35, at which point it declined concave down. Menken and colleagues make clear that their historical analyses cannot reflect the age pattern of fecundability because they could not determine how much of this decline was caused by reduced fecundability versus other age-related factors, including censoring, disease, coital frequency, pregnancy loss and obstetric injury due to prior childbearing.

Demographers have also examined subsequent fertility by age at marriage to generate estimates of the historical age patterns of sterility (the fraction of brides at each age who never subsequently gave birth). This offers something of a lower bound on the pace of age-related decline in fecundability, since all attempts to conceive among sterile individuals lead to no pregnancies. Reanalysing an earlier study using historical English parish data (Trussell and Wilson, 1985), Menken and coauthors examined subsequent fertility by wife’s age at marriage, and estimated that the historical sterility rate was about 5% at age 25 (the youngest age estimated), 20% at age 40 and about 60% at age 45 (Menken et al., 1986). Subsequent reanalyses reported lower rates of sterility by age (Eijkemans et al., 2014; Leridon, 2008).

Ultimately, Menken and colleagues concluded that neither historical nor available contemporary data could provide an unbiased estimate of the age pattern of fecundability. While demographic work on the question continued with historical data (Larsen and Vaupel, 1993; Larsen and Yan, 2000) and more contemporary data with fewer parametric assumptions (Heckman and Walker, 1990a, 1990b; Menken and Larsen, 1986), the question of by how much and when fecundability declines with age remains open.

To illustrate how selection can depress observed fecundability at later ages, we designed a life course reproductive process model – the Conception Abortion Miscarriage Birth Simulation (CAMBS) model. ⁵ It builds on the long history of mathematical and simulation models that have been deployed since the mid-20th century (e.g. Ciganda and Todd, 2022; Gottard et al., 2015; Greulich and Toulemon, 2023; Horvitz et al., 1971; Potter, 1960; Ridley and Sheps, 1966; Sheps and Menken, 1973, 1971, 1971; Sheps et al., 1969, 1969; Tietze, 1959; Udry and Poole, 1974).

In these models, individuals spend their reproductive lives in one of the following states: susceptible to pregnancy, pregnant, or non-susceptible to pregnancy due to a recent prior pregnancy (postpartum infecundability). The state of being susceptible to pregnancy is subdivided into periods of seeking and not seeking to conceive. The state of being non-susceptible to pregnancy is subdivided into periods of being non-susceptible after a live birth and being non-susceptible after a pregnancy ends in miscarriage or abortion (non-live birth). Each reproductive event is a state transition, and the probability of each event varies according to the state (e.g. the probability of a new conception is zero for the duration of a pregnancy, while the probability of a miscarriage is non-zero only during pregnancy). Some probabilities vary according to the duration in the state (e.g. the probability of a miscarriage is higher earlier in pregnancy).

The discrete time model we use is based on those in Sheps and Menken (1973) and is illustrated in Figure 1. States are shown as boxes and arrows represent transitions.

Each arrow is associated with the probability of the event that the transition represents. Transitions include: conception, miscarriage, abortion, birth, end of a non-susceptible period, and initiation of conception-seeking. Our model is weekly, with ovulation occurring every four weeks, though similar results are produced by monthly models.

Individuals stay in their state until a transition occurs, so an individual who seeks to conceive remains in the susceptible, conception-seeking state until conception is achieved. We do not model transitions out of sexual activity, so we do not include a state of non-susceptibility due to celibacy. We model celibacy before the onset of sexual activity as absence from the model. Those individuals who are not seeking to conceive are modelled as contracepting.

Simulations using reproductive process models can generate full reproductive life courses for individuals and populations, given input parameters. To investigate how selection shapes conception-seeking, we conduct simulations in which fecundability varies across a cohort of individuals but is constant for every individual as they age. We present results in which only the fecundability distribution and celibacy before the age at earliest conception-seeking vary. Assumptions for all transitions are described below. We analyse the resulting life course histories.

By observing the population initiating conception-seeking at each age in a counterfactual condition in which no individual experiences age-related decline in fecundability, we isolate the effect of selection on observed age-specific fecundability. This allows us to investigate the possible magnitude of such selection.

For each simulation, a cohort of individuals is assigned individual-level traits drawn from independent population-level distributions. Their transitions between states are determined by universal transition parameters.

Individual-level traits that remain constant over the lifetime are: fecundability, sexual activity before conception-seeking, contraceptive efficacy, age at earliest conception-seeking (the individual contracepts to delay conception or remains celibate prior to this age) and desired lifetime parity (parity at which the individual starts or resumes the use of contraception to avoid conceiving). Universal parameters include duration-dependent probabilities of abortion and miscarriage; durations of non-susceptibility to pregnancy after a miscarriage, an abortion or a birth; duration of pregnancy; and duration between birth and initiation of conception-seeking for the next desired birth. See Supplementary material available online (https://doi.org/10.1553/p-p7d2-d2hz) for more details on individual-level traits (Table S.1) and universal parameters (Table S.2).

We assign individual-level traits to each individual in a 50,000-woman cohort and then simulate each individual’s weekly reproductive life course from the week she enters the model in the state SUSCEPTIBLE (not seeking conception) (age 15 in the baseline case) until the week she turns age 50.

In the main text, we report results from simulations across which only two factors vary: population-level heterogeneity in fecundability and whether individuals engage in sexual activity before reaching their age at earliest conception-seeking.

Our analysis takes the form of reporting on the results of our simulations. For each age at last birthday, we calculate mean fecundability among those who initiate a spell of conception-seeking at that age. We calculate this mean directly based on individuals’ assigned age-invariant fecundability, and call the resulting statistic mean observed fecundability at that age. We focus on initiators at each age to minimise length bias. For further details on the target population for whom mean fecundability is observed at each age and simulation results under alternative population definitions, see Supplementary Material section S2.1.

Because the degree of population-level heterogeneity is unknown and directly salient to the selection process, we begin by displaying mean observed fecundability for our baseline simulation and the six alternative simulations of greater or lesser heterogeneity. This provides a sense of the possible magnitude of depression in mean observed fecundability caused by selection on fecundability.

To illustrate the role of births conceived before conception is ever sought (unsought births), we compare results from simulations in which all individuals are sexually active and contracept starting at age 15 with results from simulations in which all individuals are celibate until reaching their age at earliest conception-seeking. We repeat these simulations for the baseline and higher and lower heterogeneity of fecundability distributions.

Finally, we look within our baseline simulation to summarise the reproductive experiences of individuals with different fecundabilities. These results illustrate the mechanisms by which fecundability influences ages at conception-seeking.

To illustrate the changing composition of those initiating conception-seeking by fecundability, we display the relative risk of initiating a spell of conception-seeking by age last birthday and fecundability.

To illustrate how the timing of parity-specific conception-seeking varies by fecundability, we report the mean ages at which individuals begin seeking to conceive by parity and fecundability.

To provide an overview of the sensitivity of the selection process to individual-level traits, we also provide a summary figure displaying mean fecundability among those initiating spells of conception-seeking at ages at last birthday of 35–39 by trait. This figure shows how much mean observable fecundability declines by ages 35–39 by level of contraceptive efficacy, age at earliest conception-seeking and desired lifetime parity.

Figure 3 displays mean fecundability among those initiating spells of conception-seeking by single year of age at various levels of population-level heterogeneity in fecundability. In these simulations, all individuals are sexually active and contracepting starting at age 15. Population-level heterogeneity in fecundability (see Figure 2) ranges from σ = 0.01 to σ = 0.09 , and the underlying all-individual mean is μ = 0.2 , constant across ages.

The greater the heterogeneity in fecundability in the population, the greater the depression in observed mean fecundability as age advances. Observed mean fecundability changes little with age when σ = 0.01 . Consider only ages 35–39: As we take 6 steps, increasing heterogeneity from σ = 0.025 to σ = 0.09 , observed mean fecundability decreases: 0.19, 0.18, 0.16, 0.15, 0.12, 0.10. Despite population mean fecundability constant at 0.20 in all cases, increased heterogeneity leads to increased selection among women initiating a spell of conception seeking and observed mean fecundability at our highest heterogeneity is depressed to about half the population level by ages 35–39.

In Figure 4, we illustrate the effect of sexual activity before the age at earliest conception-seeking on observed fecundability by age. We compare results from simulations in which no one has sex before they seek to conceive with results from simulations in which everyone has sex starting at age 15 and contracepts unless seeking to conceive. For simplicity, we offer pairs of such simulations at three levels of population-level heterogeneity in fecundability, σ = 0.025 , σ = 0.05 and σ = 0.075 . All other factors remain the same as in our baseline simulation. For each level of heterogeneity, dashed lines reflect results of simulations in which no one has sex before reaching their age at earliest conception-seeking, and solid lines reflect the results in which sex begins at age 15.

In all six simulations, the observed mean fecundability at older ages is less depressed in the simulation with celibacy before conception-seeking than in the simulation in which all individuals are sexually active from age 15. We illustrate this by comparing across the sexual activity conditions at the same population level heterogeneity in fecundability and expressing observed means in terms of their depression from the underlying all-individual mean at ages 35–39. For example, when σ = 0.05 , in the abstinent simulation the observed mean is depressed by 11% of the underlying all-individual mean, compared with a depression of 18% in the sexually active from age 15 simulation. And when σ = 0.075 , the observed mean in the abstinent simulation is depressed by 28%, compared with a depression of 39% in the sexually active from age 15 simulation. While the overall magnitude of the depression in the observed means is small when σ = 0.025 , the depression in the simulation with celibacy is similar to the depression in the sexually active from age 15 simulation (3.0% vs 3.5% of the all-individual mean). In general, the depressions of the observed mean in the simulations with full celibacy before conception-seeking are about 70% of the depressions of the observed mean in the simulations with extensive sexual activity before conception was sought.

Next, we turn away from patterns of mean observed fecundability by age to focus on how fecundability shapes individuals’ ages at conception-seeking, generating the selection driving the patterns described above.

Figure 5 shows how the risk of initiating a spell of conception-seeking varies according to fecundability itself. These results are drawn from our baseline simulation, so all individuals are sexually active before reaching their age at earliest conception-seeking. We group individuals into ranges of fecundability 1 σ -wide and use the group with fecundability 0.15–0.2 as a comparison. For each group, we plot the log relative risk of initiating a spell of conception-seeking by age at last birthday, comparing individuals in each range to those whose fecundability is 0.15–0.20. We display relative risks only if both the index group and the comparison group had at least 50 initiations in the year of age.

The downward slope of the lines for groups with fecundabilities greater than the comparison demonstrates that individuals with higher fecundability are increasingly less likely to initiate conception-seeking with advancing age. The upward slopes of the lines for groups with fecundabilities lower than those of the comparison group demonstrate that groups with lower fecundability are increasingly more likely to initiate conception-seeking with advancing age. By the late twenties, differences begin to emerge. By age 27, the relative risks are 1.2 and 0.87 for the groups just above and just below the comparison, respectively. The divergence accelerates in the thirties, with the relative risks being 1.56 and 0.74 for the same groups at age 34. After age 35, the divergence continues to increase, particularly for the groups with lower fecundability. At age 40, the relative risk of initiating a spell of conception-seeking is 2.1 and 0.55 for the groups just above and just below the comparison, respectively.

Figure 6 illustrates parity before the age at earliest conception-seeking by level of fecundability, using results from our baseline simulation. Each column in Figure 6 describes a 1 σ -wide range of fecundability, like the lines in Figure 5. The parity composition of individuals in that range of fecundability at the earliest age at which they would seek to conceive is reflected by the colours of the bars. The lightest green reflects the fraction of individuals who had no births before they would ever seek to conceive, with darker colours reflecting one, two and three or more births. The proportion of individuals at parities one, two and three or more increases as fecundability increases because all the pregnancies leading to these births occurred due to contraceptive failures, and such failures are proportional to fecundability. Over half of those in all groups with fecundability of over 0.2 had had at least one birth before reaching their age at earliest conception-seeking, with only 37% and 30% of the groups with the highest fecundability having zero births by the time they reached the earliest age at which they would seek to conceive.

These unsought births disproportionately prevent individuals with higher fecundability from being able to contribute conception-seeking to observation, and disproportionately remove individuals with higher fecundability from observation altogether. The decline in the proportion of individuals reaching their age at earliest conception-seeking with no births is especially notable. We also note (results not shown) that some individuals reached their desired lifetime parity through unsought births before reaching their age at earliest conception-seeking. Therefore, they could never be observed initiating conception-seeking. Less than 10% of those with fecundability below 0.1 reached their desired lifetime parity via unsought conceptions. This fraction increased roughly linearly across the fecundability groups, with 29% of those with fecundability above 0.3 reaching their desired lifetime parity before reaching their age at earliest conception-seeking and therefore being unobservable as ever having tried to conceive. In relative terms, this means that those individuals with fecundability above 0.3 were three times as likely to be excluded from the observation of fecundability at any age compared with those individuals whose fecundability was below 0.1.

Table 1 displays the mean ages of individuals initiating spells of conception-seeking by parity of the birth sought and fecundability. Darker colours in the table reflect older mean ages. Lower fecundability is associated with older mean ages at the initiation of conception-seeking for parities two and greater. For example, the mean age at the initiation of conception-seeking for the second birth is 0.78 years greater at fecundability 0.1–0.15 than at fecundability 0.2–0.25. The differences are even starker between adjacent parity groups at fecundabilities below 0.15. The differences increase as parity increases. The difference in the mean age between fecundability 0.05–0.1 and 0.3–0.35 increases from 2.23 years when seeking to conceive for the second birth, to 3.16 years when seeking to conceive for the third birth and to 3.89 years when seeking to conceive for the fourth birth.

In Figure 7, we present a summary of selection across a variety of traits and factors using mean fecundability among those initiating attempts to conceive at ages 35–39. This summary compares selection across levels of contraceptive efficacy, desired lifetime parity and age at earliest conception-seeking based on the baseline simulation, as well as selection across our specifications of sexual behaviour before the age at earliest conception-seeking and heterogeneity in fecundability across simulations.

Dots that are lower on the plot reflect greater negative selection on fecundability, since the underlying all-individual mean of every group is 0.2. Black dots reflect means among individuals with specified traits. These results are not presented elsewhere. For comparison, we also summarise selection in the same way for simulations with the seven degrees of population-level heterogeneity fecundability from Figure 3 and the two simulations with σ = 0.05 in Figure 4. We follow the colour conventions from Figures 3 and 4 for the markers displaying results derived from the same simulations.

Figure 7 reflects that higher contraceptive efficacy and lower desired parity are associated with less selection on fecundability. Those individuals for whom contracepting is more effective have fewer contraceptive failures on average and are thus less negatively selected via that mechanism. Moreover, those individuals who want fewer births are impacted by selection due to waiting time to conception to either a smaller degree or not at all (if they want only one birth) compared to those who want more births. Much greater variation in selection is exhibited across ages at earliest conception-seeking. This is because fewer individuals who initially seek to conceive at younger ages remain in the pool of possible conception seekers by ages 35–39. For example, less than 0.01% of those who desired conception starting at ages 20–24 and 1.2% of those who desired conception starting at ages 25–29 were observed initiating a spell of conception-seeking at ages 35–39. Thus, while selection is very great, few of the observed initiations at later ages are from individuals who initially sought to conceive over a decade earlier. For a comparison of the magnitude, substantial variation in selection as population-level heterogeneity in fecundability increases is displayed in the figure, as is the more modest decrease in selection when all individuals practice celibacy until reaching the age at earliest conception-seeking.