Sex Selection for Daughters: Demographic Consequences of Female-Biased Sex Ratios

Modern fertility techniques allow parents to carry out preimplantation sex selection. Sex selection for non-medical purposes is legal in many high-income countries, and social norms toward assisted reproductive technology are increasingly permissive and may plausibly become increasingly prevalent in the near future. We explore possible outcomes of widely observed daughter preferences in many high-income countries and explore the demographic consequences of the adoption of sex selection for daughters. While concerns over son preference have been widely discussed, sex selection that favors female children is a more likely outcome in high-income countries. If sex selection is adopted, it may bias the sex ratio in a given population. Male-biased populations are likely to experience slower population growth, which limits the long-term viability of corresponding cultural norms. Conversely, female-biased populations are likely to experience faster population growth. Cultural norms that promote female-biased sex ratios are as a consequence therefore also self-reinforcing. In this study, we explore the demographic consequences of a female-biased sex ratio for population growth and population age structure. We also discuss the technology and parental preferences that may give rise to such a scenario.


Introduction
Preimplantation sex selection (henceforth sex selection) is a practice in which individuals attempt to control the sex of their offspring before the fertilized egg has been implanted in the uterus. The motivation for sex selection can vary, but we will here focus on sex selection for non-medical reasons. In recent decades, post-implantation sex selection (i.e., abortions and infanticide) has contributed to bias in the sex ratio in certain countries; this phenomenon has been widely discussed (Sen, 1990). Most research on biased sex ratios at birth due to parental preferences has focused on "missing women," often with a focus on Asian countries where sex selection against female children and excess child mortality among girls have been prevalent (e.g., Guilmoto, 2012;Sen, 1990). However, emerging evidence of preferences for daughters in high-income countries means that it is also interesting to examine the case of female-biased sex ratios.
In this article, we discuss the potential impact of an increase in the use of sex selection technology from a different perspective, based on three recent developments: • Sex selection technologies are now legal, non-invasive, and relatively inexpensive in many high-income countries. • In high-income countries, prospective parents have, on average, a preference for female children. • In most high-income countries, single women 1 and women in same-sex relationships have unprecedented legal and financial access to assisted reproductive technology (ART).
We note that unlike a male-biased sex ratio, which tends to depress population growth (Johnson, 1994), a female-biased sex ratio will increase population growth (ceteris paribus). In this article, we explore the demographic consequences of female-biased sex ratios at birth and show that they may be considerable under certain assumptions. 2 We use analytical demographic models to illustrate different scenarios with different extent of female-biased sex ratios, under different fertility regimes. We show how biased sex ratios may affect number of births and population growth (r in a demographic or population genetics model), through a cultural evolutionary process.

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Sex Selection for Daughters: Demographic Consequences of… Background Three techniques are currently used for the purpose of sex selection. The first two are relatively invasive, expensive, and associated with non-negligible medical risk. We mention these in contrast to the third technique.
Ultrasound in combination with abortion is a prenatal rather than a preimplantation technique for sex selection and is thus more invasive and associated with considerable medical risk. The sex of the fetus can be detected with ultrasound at week 11, at the earliest, which means that abortions may have medical risks, especially in low-income countries (Igbinedion & Akhigbe, 2012). 3 While this remains the most prevalent technique for sex selection in low-and middle-income countries (mostly used to select male children), it is rarely used in high-income countries. We do not foresee this as a common or preferred method for sex selection in high-income countries in the future; thus, we will not discuss this technique in any further detail.
Preimplantation genetic diagnosis (PGD), a practice where an embryo is screened in vitro before implantation in the uterus, is used to some extent for sex selection in high-income countries. PGD is highly accurate in determining the sex of the embryo (Harper & SenGupta, 2012;Sermon et al., 2004). However, since PGD requires in vitro fertilization (IVF), it is relatively expensive and invasive, as it requires hormonal ovarian stimulation and retrieval of eggs from the ovaries. Thus, PGD is typically motivated by medical sex selection: for example, if the parents have a hereditary medical condition that only affects one sex. However, as a larger share of parents use IVF for reasons other than sex selection (Kupka et al., 2014), more parents will be able, at little additional cost, to choose the sex of their child if they so desire.
Flow cytometry is a relatively novel technique that is far less invasive and costly than the other two. Here, semen is labeled with a fluorescent dye that binds to the DNA of each spermatozoon (Sharpe & Evans, 2009). As the X chromosome is larger (i.e., contains more DNA) than the Y chromosome, "female" (X-chromosome bearing) spermatozoa will absorb a greater amount of dye than their "male" (Y-chromosome bearing) counterpart. Consequently, when exposed to UV light, "female" spermatozoa fluoresce brighter than "male" spermatozoa. As the spermatozoa pass through the flow cytometer in single file, each spermatozoon is encased by a single droplet of fluid and assigned an electric charge corresponding to its chromosome status (X-positive charge or Y-negative charge). The stream of X-and Y-droplets is then separated using electrostatic deflection and collected into separate collection tubes for subsequent processing (O'Neill et al., 2013;Reubinoff & Schenker, 1996). This method does not require IVF and can be used in combination with insemination. While this method is less invasive than PGD, it is also (somewhat) less accurate. In a study from 2014, 95% of babies born were females after sorting for X-spermatozoa and 85% were males after sorting for Y-bearing spermatozoa 1 3 (Karabinus et al., 2014). The technique is more accurate when selecting female children than male children (Karabinus et al., 2014).
Sex selection is legal and in use in some high-income countries, including the U.S. (Bhatia, 2018). However, the most prevalent technique for sex selection in high-income countries, PGD, requires IVF, and the extent to which this is available for non-medical purposes varies. The U.S. has a very permissive regulatory regime, allowing the so-called "fertility tourism" from other countries where sex selection is only allowed for medical purposes (Whittaker, 2011). However, with the increasing popularity of flow cytometry, access to sex selection is also likely to increase. No high-income country has banned flow cytometry, and a ban on insemination of sorted sperm is likely to be difficult to enforce. The company MicroSort, which uses flow cytometry and offers non-medical sex selection services, already operates in Mexico, Malaysia, North Cyprus, and Switzerland, attracting fertility tourism (MicroSort, 2020).
Since the first IVF procedure in 1978, ART has become widespread and widely accepted. In the U.S., more than 55,000 women per year give birth to a baby conceived through ART (IVF or insemination; Dusenbery, 2020). Moreover, public support for this technology has also increased considerably, with ART now subsidized by public healthcare systems in many high-income countries for infertile differentsex couples, single mothers, and female same-sex couples.

Sex Preferences in High-income and Middle-income Countries
Recent research in sociology and demography has found increasing preferences for female children in high-income countries. This has mostly been expressed through parents more often having higher-order births if their previous children were either lacking sons or daughters, but there is also increasing evidence for parents explicitly wanting daughters when they have more direct choice over their reproduction. Below, we summarize the recent research on sex preferences in high-income countries.
Most of the existing research on sex preferences and fertility outcomes has focused on countries with strong son preferences. In particular, in East and South Asia, where patrilineal kinship systems are common, parental preferences for male children have been commonplace in both contemporary and historical societies (Arnold & Zhaoxiang, 1992;Drixler, 2013;Guilmoto, 2012;Mungello, 2008;Sen, 1990). Such preferences have historically been associated with elevated female child mortality and infanticide, with major demographic impact (Arnold & Zhaoxiang, 1992;Drixler, 2013;Guilmoto, 2012;Mungello, 2008;Sen, 1990). Beginning in the 1980s, the availability of ultrasound combined with abortion led to elevated male sex ratios across East Asia, South Asia, Caucasia, and some other countries such as Albania and Tunisia (Chao et al., 2019;Guilmoto, 2009). A preference for male children has also been historically common throughout Western Europe, but with only limited effects on child mortality or fertility outcomes (Kolk, 2011;Sandström & Vikström, 2015;Tsuya et al., 2010). While a preference for sons seems to be a more important determinant of childbearing decisions globally (Arnold, 1997;Guilmoto & Tove, 2015), in high-income countries, the picture is notably different, with increasing evidence of a preference for daughters and for a mixed-sex composition (Kolk & Schnettler, 2013;Miranda et al., 2018). This trend is not only prevalent in Western countries but has also been observed in Japan (Fuse, 2013). Also, in middle-income regions traditionally dominated by strong son preferences, such as rural China, there is some novel evidence that some parents are developing a preference for daughters over sons (Shi, 2017). In high-income countries, sex preferences are not expressed through biased sex ratios at birth; however, the sex composition of previous children has a strong impact on parity progressions (the decision to have a subsequent child). Across Europe and the U.S., research has shown that transition to higher-order births is influenced by the sex composition of previous children (Anderson et al., 2007;Blau et al., 2020;Hank, 2007;Hank & Kohler, 2000). A pattern in which parents prefer children of each sex is increasingly common; it is strongest for the transition to a third child, where a transition to a third child is least prevalent for parents with a son and a daughter (Hank & Kohler, 2000;Miranda et al., 2018). It should be noted here that, while they are a clear marker of parental sex preferences and the distribution of sons and daughters within families, sex-biased parity progressions (as described above) do not affect the overall sex ratio in a population.
Interestingly, in Nordic countries, while a preference for mixed-sex composition remains the dominant pattern, evidence points to more parents displaying daughter preference over son preference (Anderson et al., 2007;Miranda et al., 2018;Kolk & Schnettler, 2013). For parents with one child, 35% of parents who had a son preferred their second child to be a girl, whereas only 23.4% of parents who had a daughter preferred their next child to be a boy (Miranda et al., 2018). For parents with a daughter, 74% said the sex of the next child did not matter, compared to 58% for those with a son. Demographers have previously speculated that high gender equality would lead to parental sex indifference, whereby the sex composition of previous children would not affect the decision to have subsequent children (Pollard & Morgan, 2002). In reality, however, this seems not to be the case; instead, we find that in countries that are the most equal, it appears more common for parents to prefer female children (Andersson et al., 2006;Miranda et al., 2018). It is thus conceivable that increasing gender equality will, if anything, lead to daughter preference becoming more widespread. Moreover, in Japan, traditionalism and adherence to traditional gender roles among women have also been predictive of daughter preferences (Fuse, 2013), suggesting that-with increasing female agency over fertility-we may also see greater daughter preference in less gender egalitarian contexts (see also Shi, 2017). In some sub-Saharan countries such as South Africa, researchers have also observed some evidence of a daughter preference giving rise to femalebiased sex ratios among young children (Marco-Gracia & Fourie, 2019), though this seems to originate from sex-selective investment rather than pre-birth sex selection. Other researchers have also observed emerging daughter preferences and suggested it may be linked to greater expectations that daughters will take care of them in old age, as well as the notion that women tend to do better in contemporary western educational systems (Blau et al., 2020;Shi, 2017).
Evidently, although most heterosexual parents in Western countries have not acted to deliberately affect the sex of their children, their behavior following the (random) allocation of previous births has a clear impact on their subsequent behavior. In the less prevalent contexts where potential parents already have direct agency over the sex of their children, we find stronger evidence of parental preferences for daughters. For several decades, adoptive parents have, on average, shown a strong preference for female children, an interesting illustration of a scenario in which parents to some extent can choose the sex of their children (Högbacka, 2008). However, sex and other aspects, such as the ethnic match of the child and the parents, interact in complex ways in international adoption (Högbacka, 2008). In a sample of infertile women considering ART treatment, 40% responded positively about choosing the sex of their child if the option to do so was offered at no additional cost (Jain et al., 2005). Among women who wanted to select the sex of their future child, 39% wanted a male child, and 61% wanted a female child (Jain et al., 2005). Of women considering ART treatment, it was much more common to express a daughter preference than a son preference, although women who already had children had a preference for a mixed-sex composition (Jain et al., 2005). Lamberts et al. (2017) found higher rates of vasectomy among men with more sons than daughters. Overall, it seems that when more choice, technology, and agency are associated with the process of having a child (as opposed to children conceived through intercourse in heterosexual unions), more parents accept and consider the option of choosing the sex of their children. When parents explicitly consider the choice of sex of their future children, a daughter preference seems more common. Most children are reared by different-sex couples. In the research on sex preferences of partnered men and women, prospective mothers are seen to have a relatively higher preference for female children, whereas prospective fathers have a relatively higher preference for male children (Higginson & Aarssen, 2011;Lynch et al., 2018). This sex-biased pattern is found in societies with both son preference and daughter preference on average (van Balen, 2006). This suggests that the preference for children of one's own gender is a relatively general pattern across cultures. There is little research knowledge about sex preferences among single women and samesex female couples, although some studies indicate that heterosexual single women and women in same-sex couples more often exhibit daughter preference (Gartrell et al., 1996;Goldberg, 2009;Leiblum et al., 1995). If women across all union types have a preference for daughters one would expect single women and female samesex couples to be able to act on this preference without negotiating with a male partner and therefore on average engage more readily in sex selection. In general, groups who are more likely to use ART for non-sex-selective reasons, such as people with fertility concerns, single women, and women in same-sex relationships, may more often choose sex selection, because sex selection (either via PGD or flow cytometry) is a relatively straightforward addition to ART procedures (van Balen, 2006). In summary, previous research has found increasing evidence of a daughter preference in high-income countries. In situations where parents have more direct choice over the sex of their children, such as adoption and IVF, we also find stronger daughter preferences. Overall, we argue that a latent daughter preference is apparent in highincome countries, and that this is stronger among women than men.

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Sex Selection for Daughters: Demographic Consequences of…

Analytical Approach
To estimate how female-biased sex ratios may affect population growth, we present calculations for different countries with different sex ratios and show how the sex ratio affects population growth rates and age structure.
Our calculations are based on two important assumptions. First, since we are interested in the long-term effects of changing sex ratios, we therefore show the long-term equilibrium effect of a change in sex ratios given a set of assumptions on fertility and mortality. This is what demographers refer to as a stable population (Wachter, 2014, pp. 218-249). It is worth stressing that we apply reductionist and commonly used demographic approximations to our demographic examples so that they may be more easily followed, instead of more technical models. All our calculations refer to the long-term consequences for a population with the same fixed behavior over multiple generations; as such, they are only useful to illustrate the long-term implications of female-biased sex ratios. They are not useful for predicting actual demographic outcomes in the near future. Given the uncertainties in the extent of uptake (and timing of uptake) of the behaviors we discuss here, focusing on the large-scale demographic influence of these trends is more relevant than trying to forecast near-future empirical scenarios.
Second, our models follow the standard demographic methodology in which demographic analysis is based on female reproductive choice in a society. This is the approach used in most standard demographic analysis (e.g., Wachter 2014, pp. 79-89). However, certain assumptions in such models, such as the implicit assumption that (male) co-procreating and co-childrearing partners are unconstrained, are less realistic in cases with highly biased sex ratios. We discuss whether these assumptions can be analyzed independently of the overall sex ratio later in section 'Will there be Counteracting Mechanisms to Sex Selection' as well as other factors that may stabilize the sex ratio given a preference for female births. We also analytically calculate the age structure implications of different fertility scenarios with different sex ratios, showing that in some scenarios of high total fertility and highly biased sex ratios, it is relevant to assess demographic support ratios. Some previous demographic literature on male-biased sex ratios has created demographic models exploring how male preferences and male sex ratios affect population growth (Bennett, 1983;Leung, 1994;Mason & Bennett, 1977), finding that male-biased sex selection would decrease population growth.
We only show results for the average sex ratio over all women in a population. Previous models have shown that even when a relatively small group of parents use sex-selective technology, the impact on population level sex ratios can be considerable (Dubuc & Sivia 2018;Kashyap & Villavicencio, 2016). Throughout our results, we present the ratio of the female share of all births, instead of female births over male births (the traditional measure of sex ratios), as that is the input to our models. All data and calculations are available in a spreadsheet (supplemental file 1: data and calculations).

Consequences of Biased Sex Ratios for Population Growth
We begin by examining changes to population growth arising from different assumptions of fertility and share of female births. In Eq. 1, we show the net reproductive rate based on a given ratio of female births over all births , mortality pattern ( l x ), and fertility pattern f x , using 5-year age group life tables. The net reproductive rate can be interpreted as a multiplier of each subsequent generation; a value above 1 thus indicates a population where every generation is larger than the previous one, and a value smaller than 1 indicates a shrinking population. A value of 1.5 indicates that each new generation is 50% larger than the preceding one.
In Eq. 2, we show the Dublin-Lotka approximation, which shows how a given net reproductive rate translates into yearly population growth (r) based on the mean age of reproduction in a population (T), which can be calculated from f x .
Together, these two equations give a good approximation of how a given share of female births, mortality pattern, and fertility pattern jointly determine long-term growth in a given population. We largely focus on share of female births and fertility here, as different mortality assumptions make little practical difference to contemporary populations in high-income countries. We use a single mortality pattern in all examples, based on the pattern in the U.S. for 2017. Survival up to age 45 is today so high, even in lower-middle income countries, 4 that it plays only a minor role in generational reproduction, and we do not expect this to change in the foreseeable future.
We illustrate the consequences of changing the share of female births with a selection of different assumptions on the average number of births per woman in a population (or Total Fertility Rate, TFR). The different fertility scenarios are: very low (Taiwan 2014, TFR = 1.16); somewhat typical for an OECD country (U.S. 2017, TFR = 1.76); high (Kenya 2014, TFR = 3.90). In our supplemental materials, we also include a traditional fertility schedule used for populations that are close to the highest observed fertility in human populations, the Hutterites in the U.S. in the 1920s (TFR = 10.31; see Henry, 1961, from where we get our fertility schedule). We collected mortality data for the U. (1) In Table 1 (upper panel), we show the consequences of different ratios of female share of all births for population growth (r) using the approximations from Eqs. 1 and 2 with different fertility rates. We show fertility patterns for three different countries. We show a scenario where the female share of all births is 48 daughters of 100 total births (which is close to what is naturally occurring in contemporary populations; see James, 1987), as well as a scenario with a share of female births of 60 5 and 80 daughters per 100 births.
Equation 3 shows how yearly population growth (r) corresponds to initial and final population size ( P 0 and P n , respectively) over n years. We use Eq. 3 to translate how the population growth rate in Table 1 (lower panel) translates into population growth over 50 years. This represents how much larger a population would be after 50 years of corresponding population growth, given that the fertility rates, mortality rates, population growth, and the female share of births would be fixed and at equilibrium.
(3) P n = (1 + r) n P 0  Kashyap and Villavicencio (2016) and Dubuc and Sivia (2018) that show that you can get (male) biased sex ratios even if relatively few parents use sex-selective technology.
As we can see from the table, changing the sex ratio has a significant impact on population growth. 6 While the prevailing fertility schedule and observed share of female births in the U.S. will lead to a reduction in the population by around 30% (the equilibrium consequences of contemporary demographic rates over 50 years), when we compare this to a population where an assumed 60% of all births are female, the population would instead surge by 7%. In turn, a population where 80% of births are female would increase by 78% over 50 years. With prevailing fertility rates and an unbiased share of female births, Taiwan's current fertility schedule implies that such a population will contract by 66% over 50 years; given a sex ratio of 80% women, it would only contract by 16%. In Kenya, a share of 80% (rather than 48%) would result in an increase of over 600% (compared to the already considerable increase of nearly 200%) over 50 years. With the higher fertility of the Hutterites shown in the supplemental materials (supplemental table S2), these increases are even more dramatic (and so high to be unrealistic in a real population). Note once again that these are equilibrium scenarios used to explore differences for changing share of female births and not as demographic forecasts; here, we use constant demographic rates and contemporary constant U.S. mortality patterns to illustrate how changing sex ratios interact with different fertility assumptions.

Consequences of Biased Sex Ratios for Population Age Structure
In the following section, we explore the consequences for the age structure of the population given the scenarios outlined above. In human societies, children and infants are provided resources and care by adults (to a large extent their parents), and in contemporary high-income societies, elderly individuals also provide substantial support. The importance of lifecycle transfers to the age structure of a population has been widely recognized in anthropology, economics, and evolutionary biology, where it forms the basis of life course theory (Kaplan, 1994;Lancaster et al., 2000;Lee & Mason, 2011).
The high population growth rates illustrated in Table 1 produce a high share of young dependents in the population in the long term, which we illustrate in Fig. 1. The calculations are based on the same fertility and mortality schedules as in Table 1. The stable age structure of a population under a given r and l x is given by Eq. 4 (the Euler-Lotka equation in discrete form for 5-year age groups, see Slogett, 2015), where l x is the remaining life years at age x, and the numerator is the share of life years at time x, divided by the denominator, which is the sum of all life years in the population up to age ⍵. From the stable population equations, we can calculate the age distribution and show population pyramids by sex for our different scenarios. Using the age structure calculated from Eq. 4, we also show various measures of demographic dependency. 7 1 3   Table 1. It shows the eventual equilibrium age structure if fertility and mortality rates remain constant indefinitely in the 0-19 population and assuming that each life year of a child needs a third of an adult's life year for education, child rearing, procreation, etc. The exact input a child needs will of course vary according to culture and context, and the value of 1 ∕3 is only for illustration. We then divided the sum of time needed to take care of the young population by the available time in the adult population to obtain a rough estimate of how much of all productive (and leisure) time of the population aged 20-64 (a 0-19 × 1 ∕3 /a 20-64 ) must be spent on rearing the subsequent generations. We make the second calculations both for men and women and the denominator, and for only women in the denominator.

Footnote 7 (continued)
It is clear from Fig. 1 that very high population growth rates (as seen in Table 1) cause a very young age structure. In the U.S., current fertility rates and share of female births imply a shrinking population (from natural growth) with an old age structure, while similar fertility rates with 60% female births would instead result in a growing population with a younger age structure. Across the different populations shown in Fig. 1, it is clear that a higher share of female births results in higher population growth, a higher share of women (naturally), and more resources that will have to be spent on supporting and rearing the young. For the U.S., with moderate/ low fertility, the impact of age structure on different dependency ratios (see Fig. 1) is relatively small and may even be beneficial. With Kenyan fertility levels, on the other hand, the high population growth and corresponding young populations with a high share of female births would have consequences for the ability of adult members of society to adequately support the younger generations. In the online Appendix S1 (Table 2 and Figs. 3 and 4), we explore growth rates and equilibrium age structure from other demographic scenarios including very skewed share of femalebiased births, male-biased births, and very high fertility rates.

Will Sex Selection Become Widespread in High-income Countries?
It should be noted that many people still express disapproval of non-medical parental sex selection, even with novel methods such as flow cytometry (Ethics Committee of the American Society for Reproductive Medicine, 2015). In a general population survey in the U.S. in 2006, only 18% of individuals aged 18-45 said they were positive, and 22% were undecided, if they had the option to use a cost-free, risk-free, non-invasive method to choose the gender of their child (Dahl et al., 2006). While most parents express a preference for a "balanced" family (i.e., at least one child of each sex), parents with one son are keener to do so than those with one daughter (Miranda et al., 2018).
On the contrary, we may have reasons to believe that the use of sex selection technologies will become more prevalent in the near future. According to a 2017 survey, 77% of fertility clinics in the U.S. that offer PGD also offer sex selection for non-medical reasons, which represents a substantial increase from 2006, when only 42% of clinics that offered PGD offered non-medical sex selection (Capelouto et al., 2018). Flow cytometry in combination with insemination is more affordable and less risky than PGD (which requires IVF) and less likely to be seen as morally objectionable, as it does not involve the discarding of fertilized eggs, meaning that access to this technology is likely to increase the use of sex selection in the general population.
Technologies associated with reproduction, including ART but also contraceptives of various kinds, have been highly controversial when introduced, and some remain so. However, we have consistently seen that attitudes toward different reproduction technologies have become gradually more liberal over time. For example, IVF was once considered a highly divisive procedure. In the spring of 1972, the British magazine Nova ran a cover story suggesting that "test-tube babies" were "the biggest threat since the atom bomb" (Eschner, 2017;Henig, 2003). We can reasonably expect that at least part of current aversions to sex selection is due to a similar "yuck effect," which tends to dissipate as the use of the technology in question becomes normalized. Indeed, van Balen (2006) has described the technological trend toward more accessible, less invasive means of choosing the sex of a child as "nearly inevitable," and that any governmental countermeasures are likely to be largely ineffectual. We think it is plausible that the eventual prevalence of sex selection will be based primarily on the preferences among parents, rather than any technological barriers.
Some objections to sex selection concern some of the techniques used for this purpose. For example, those who object to abortions naturally also find their use as a means of sex selection objectionable. This "pro-life" stance sometimes also includes objections to IVF, especially when it involves the destruction of embryos. This makes the use of PGD for the purposes of sex selection an unattractive option. However, the use of flow cytometry does not involve killing a fetus or destroying an embryo and may therefore find less opposition among "pro-life" campaigners than other forms of sex selection.
In sum, we argue that the combination of a latent and increasing daughter preference, new technology that facilitates sex selection (including flow cytometry), and increasing acceptance of ART in general suggest that sex selection is likely to become more prevalent in high-income countries over the coming decades.

Can Sex Selection be a Self-reinforcing Practice?
In the study of cultural evolution, it has been noted that certain phenomena are selfreinforcing and increase in prevalence over time. By contrast, other practices are self-limiting, in the sense that they produce outcomes that make them less prevalent or attractive. The phenomenon of sex selection may not only affect population growth directly (as demonstrated in Section "Results") but also have intergenerational consequences over multiple generations. For most practices, it can be observed that children are more likely to resemble and copy the behavior of their parents than that of unrelated members of society (Bussey & Bandura, 2004). If this also applies to norms and fertility practices, this will affect how prevalent the preference is in the next generation, as those parents who have fertility preferences that promote population growth will have more children, and those children will (often) share their parents' preferences (Kolk et al., 2014).
A practice can be self-reinforcing at both an individual and a group level (Murphy & Wang, 2001). For example, if individuals with a certain trait (e.g., a preference for having many children) have more children, and those children in turn also have that trait, the preference for having many children will increase in prevalence over time. Likewise, a group (e.g., a religious group or an ethnicity) where membership is inherited across generations will also increase in relative prevalence if its members have more children on average. In both cases, the practice will become more common in the population over time. In the context of this study, we argue that the practice of using sex selection technologies to select female children in highincome countries could become a self-reinforcing process, both at a population and a sub-population level, in ways that the practice of selecting male children in some countries has not.
As shown above, populations with female-biased sex ratios have higher rates of population growth. As a population grows, the norms and practices of that population become more prevalent, all other things being equal. By contrast, selecting male children reduces population growth, and thus over time reduces the global impact of the norms of male-biased populations. 8 Parents with an unusually strong preference for daughters may therefore decide to use sex selection, and then their daughters (and possibly sons) will themselves be more likely to sex-select than their peers.
This mechanism may be reinforced if the social learning of practices and norms is itself sexually biased (Bandura & Walters, 1977;Bussey & Bandura, 2004). In other words, daughters may be more influenced in their reproductive choices by their mothers than by their fathers (Murphy, 1999). This means that women who more strongly prefer daughters are more likely to have offspring that will inherit this daughter preference. For example, assume that women in a population either want to select daughters or do not. Both will have the same number of offspring, but the women that select daughters are going to have more daughters and thus are more likely to transfer their preference for female sex selection to their offspring than the women that do not select daughters. Moreover, since our model assumes that having more daughters leads to higher population growth, the women that select for daughters are going to have more grandchildren than women that do not select daughters. These grandchildren are also more likely to be daughters than the grandchildren of women that do not select for daughters, and they are more likely to inherit the preference for sex selection. In other words, the norms that are conducive of female sex selection are both adaptive in a demographic/natural selection perspective (a higher r) (since they produce a larger number of grandchildren) and create more "vessels" (i.e., daughters) for spreading those norms.
Moreover, since women on average have a stronger preference for daughters than men, in each generation daughter preferences (and selection for daughters) may become more common as women become a larger share of the population. This will be particularly true for the increasing share of women who choose to have children without a male co-parent, either as single mothers or in same-sex couples. If these groups both have more daughters than the average individual in a society, and their children share their preferences for sex selection, both the share of women raising children without men and the practice of sex selection may increase accordingly.

Sex Selection for Daughters: Demographic Consequences of…
The cultural evolutionary logic above suggests that even if only a small minority of a population is positively dispositioned to sex selection, mechanisms exist through which this practice could become increasingly commonplace in each subsequent generation. If the self-reinforcing dynamic of this process proves to be correct, we should expect that populations with a female-biased ratio will be increasingly common in high-income countries. However, it is possible to make the case for a limit to an ever-increasing prevalence of sex selection, which we explore in the following section.

Will There be Counteracting Mechanisms to Sex Selection?
When assuming higher population growth among populations with female-biased sex ratios, we have used demographic calculations in which the availability of male partners is completely independent of the fertility rates of women in the population. This is common in demographic analysis, but such cases typically do not foresee very biased sex ratios. Similarly, in the above section, we highlighted a mechanism by which the female sex ratio would continue to increase. Both assumptions that (a) the sex ratio will not affect the age-specific fertility rates for a female in a population and (b) a cultural evolutionary mechanism will steadily increase the preference for female sex selection are almost certainly unrealistic for scenarios that deviate significantly from a balanced sex ratio. Indeed, at some level of bias in the sex ratio, it is reasonable to expect that other societal mechanisms may counteract these trends. Below, we discuss such possibilities, beginning with arguments from evolutionary biology on why sex ratios tend to be balanced by natural selection and why this is not the case in our scenario with ART, followed by other mechanisms that nevertheless will also eventually balance the sex ratio at some level.
In species with sexual reproduction that are under natural selection, share of male and female births is close to 50-50 through self-adjusting evolutionary processes. The evolutionary mechanisms according to which offspring of the sex that is temporarily underrepresented will have greater reproductive success is known as Fisher's principle (Hamilton, 1967). However, this logic that appears without few exceptions for natural selection is not applicable to the opportunity to procreate in our scenario, since ART removes the link between reproductive success and the sex ratio for women (i.e., as long as there is minimal number of men in the population, female reproduction is independent of the sex ratio). Nevertheless, the self-balancing mechanisms related to childrearing described in our first and second objections can be seen as analogous scenarios through which a sex ratio would be stabilized at an equilibrium, thereby stopping a process that would otherwise gradually increase the share of women.
A first counterargument is that while the biological/technological constraints of sex selection may be relaxed with the help of ART, as long as most childbearing takes place in different-sex partnerships, a deficit of males will constrain childrearing, availability of fathers, and eventual fertility rates. Traditional demographic models (including ours) assume that women are largely unconstrained by the availability of male partners for their fertility choices. This may be reasonable for share of female births close to 50-50, but it becomes increasingly implausible with very unbalanced sex ratios, even if ART removes the biological necessity of males for female childbearing. We find it plausible that a male deficit would eventually make very unbalanced sex ratios unlikely, though we note that it does not apply to single mothers or to female same-sex relationships. Indeed, as we have noted, the same cultural processes that increase the female sex ratio may also increase the share of women that choose to procreate and rear children without men.
A second mechanism that may counteract a very large share of women in a population is how societies need to adjust the ways in which they provide resources for children. As we show in our results, very rapid population growth leads to unbalanced dependency ratios between the young and adults. Similarly, if an increasing share of women choose to raise daughters by themselves, it seems likely that a single woman raising a child alone would settle for, on average, fewer children than what a couple would. Similarly, in a female same-sex relationship, the desired number of children per woman is very likely to be lower than that in a different-sex relationship; this is clear from the demography of same-sex parenthood shown by Kolk and Andersson (2020).
A third objection is that people may find a very unbalanced sex ratio "unnatural" or "disagreeable." More recently, feminist scholars have also objected to this practice. For example, Arianne Shahvisi (2018) argues that sex selection for the purposes of "family balancing" entrenches heteronormative stereotypes and misuses the moral mandate of reproductive autonomy. Elsewhere, Strange and Chadwick (2010) contend that prohibitive legislation against non-medical sex selection is justified because sex selection promotes restrictive conceptions of sex, gender, and family. Ultimately, if societies find an unbalanced sex ratio undesirable, they may adjust social policies to make such outcomes less likely. It is also plausible that parental preferences themselves may become increasingly less daughter-biased if we see a very biased female sex ratio. The preferences we see in high-income countries for a moderate daughter preference may look quite different if the sex ratio is strongly biased toward females. For example, the relative value of male children, from the perspective of parents, is likely to increase if men are scarce in a population (cf. Aksan, 2021;Diamond-Smith & Bishai, 2015, that describe the reverse case with scarce women).
A fourth objection is that our model assumes that female preferences for the number of children will remain constant (for example, at two children per woman), regardless of the sex ratio. This seems unlikely, especially in female same-sex relationships and perhaps to a lesser extent among single mothers. However, it is more likely that the average preference for the number of children will be reduced by less than the ratio of women in the population will increase. Assume an unrealistic scenario where the female share of births is 100%. To offset the increase in fertility in this scenario the average woman would have to reduce the number of children they prefer by 50%. Any reduction smaller than that would result in an increase in the population growth.
Taken together, the arguments above suggest that the potential cultural mechanisms that would increase the share of women in the population are more likely to have a moderate rather than substantial effect on the future equilibrium sex ratio, even if daughter preference becomes increasingly widespread, since counteracting mechanisms may limit the prevalence of sex selection for daughters. Based on the arguments above, we find it plausible that female-biased sex ratios will eventually reach equilibrium and that this equilibrium will not be particularly extreme. However, we do not know at which point this equilibrium will be reached.

Conclusions
The desire to select the sex of one's children is ancient in origin. In recent decades, selective abortions have mostly been used in low-and middle-income settings, and overwhelmingly to select male children. More recently, modern technology has made sex selection an inexpensive and non-invasive possibility that is less fraught with moral and medical concerns than abortion. We have argued that current trends suggest that this technology will become more accepted and more widely used over time in high-income countries, where parents now seem to prefer female children over male children. Whether this turns out to be true is uncertain, but will depend on social trends and norms, the development of which is difficult to predict. Significantly, however, it would appear that governments can do little to restrict the use of flow cytometry, as doing so would involve legally unlikely infringements on bodily autonomy. We have also argued that if sex selection technology were to become routinely used to select female children, this practice may have a self-reinforcing dynamic, potentially leading to a consistent and durable bias in the sex ratio. In our results, we described how such a sex ratio may affect population growth and the age structure, concluding that such effects are substantial and could help reach replacement rate fertility in high-income countries, while it would lead to rapid growth in countries with higher fertility.
The argument presented here is by its very nature speculative and based on the kind of uncertainty always associated with forecasting trends, but we argue that it also presents a plausible scenario. Our demographic calculations are not based on the empirical scenarios we consider most likely; rather, they aim to illustrate that the process will, over many generations, lead to substantial effects on demographic outcomes. While we do not foresee such demographic impacts to be substantial in the short term, over a longer time horizon their ramifications may be larger. If uptake of sex selection technology is small or moderate (which is plausible), the demographic effect may still be substantive. If used at lower frequencies, the dynamic effects that counteract a linear impact between sex ratios and population growth will also be less important, and a more linear relationship between more females and higher fertility will be observed. Ultimately, the aim of this article has not been to argue in favor or against the use of this technology, but to highlight its social impact over the long term. As our analysis makes clear, the consequences for population growth and social dynamics may be considerable over longer timescales.